—N-HET is selected from structures I(d) to (If):

R¹ is a (1-4C)alkyl group;

Q is selected from Q1 to Q6:

R² and R³ are independently selected from H, F, Cl, CF₃, OMe, SMe, Me and Et;

T is selected from the groups (TA) to (TE);

(TA) T is selected from the following groups:

(TAa) AR1 or AR3; or

(TAb) a group of formula (TAb1) to (TAb6):

R⁶ is independently selected from hydrogen, (1-4C)alkyl, (1-4C)alkoxycarbonyl, (1-4C)alkanoyl, carbamoyl, and cyano;

R⁴ and R⁵ are independently selected from hydrogen, halo, trifluoromethyl, cyano, azido, nitro, (1-4C)alkoxy, (1-4C)alkylS(O)_q— (q is 0, 1, or 2), (1-4C)alkanoyl, (1-4C)alkoxycarbonyl, benzyloxy-(1-4C)alkyl, (2-4C)alkanoylamino, hydroxyimino, (1-4C)alkoxyimino, —CONRcRv, and —NRcRv wherein any (1-4C)alkyl group contained in R⁴ and R⁵ is optionally substituted with up to three substituents independently selected from hydroxy and azido (excluding C1 of an alkoxy group and geminal disubstitution), oxo, trifluoromethyl, cyano, nitro, (1-4C)alkoxy, (2-4C)alkanoyloxy, hydroxyimino, (1-4C)alkoxyimino, (1-4C)alkylS(O)_q— (q is 0, 1, or 2), (1-4C)alkylSO₂—NRv-, (1-4C)alkoxycarbonyl, —CONRcRv, and —NRcRv (excluding C1 of an alkoxy group and geminal disubstitution); wherein Rv is hydrogen or (1-4C)alkyl;

R⁴ and R⁵ may further be independently selected from (1-4C)alkyl {optionally substituted with up to three substituents independently selected from hydroxy or azido (excluding geminal disubstitution), oxo, trifluoromethyl, cyano, nitro, (1-4C)alkoxy, (2-4C)alkanoyloxy, hydroxyimino, (1-4C)alkoxyimino, (1-4C)alkylS(O)_q— (q is 0, 1, or 2), (1-4C)alkylSO₂—NRv-, (1-4C)alkoxycarbonyl, —CONRcRv, and —NRcRv (excluding geminal disubstitution); wherein Rv is hydrogen or (1-4C)alkyl}; and any (1-4C)alkyl group contained in the immediately preceding optional substituents (when R⁴ and R⁵ are independently (1-4C)alkyl) is itself optionally substituted with up to three substituents independently selected from hydroxy (excluding C1 of an alkoxy group and geminal disubstitution), oxo, trifluoromethyl, cyano, nitro, (1-4C)alkoxy, (2-4C)alkanoyloxy, hydroxyimino, (1-4C)alkoxyimino, (1-4C)alkylS(O)_q— (q is 0, 1, or 2), (1-4C)alkylSO₂NRv-, (1-4C)alkoxycarbonyl, —CONRcRv, and —NRcRv (excluding C1 of an alkoxy group and geminal disubstitution); wherein Rv is hydrogen or (1-4C)alkyl; or

R⁴ is selected from one of the groups (TAba) to (TAbc) below, or one of R⁴ and R⁵ is selected from the above list of R⁴ and R⁵ values, and the other is selected from one of the groups (TAba) to (TAbc) below:

(TAba) a group of the formula (TAba1)

wherein Z⁰ is hydrogen or (1-4C)alkyl;

X⁰ and Y⁰ are independently selected from hydrogen, (1-4C)alkyl, (1-4C)alkoxycarbonyl, halo, cyano, nitro, (1-4C)alkylS(O)_q— (q is 0, 1, or 2), RvRwNSO₂—, trifluoromethyl, pentafluoroethyl, (1-4C)alkanoyl, and —CONRvRw [wherein Rv is hydrogen or (1-4C)alkyl; Rw is hydrogen or (1-4C)alkyl]; or one of X⁰ and Y⁰ is selected from the above list of X⁰ and Y⁰ values, and the other is selected from phenyl, phenylcarbonyl, —S(O)_q-phenyl (q is 0, 1, or 2), N-(phenyl)carbamoyl, phenylaminosulfonyl, AR2, (AR2)-CO—, (AR2)-S(O)_q— (q is 0, 1, or 2), N-(AR2)carbamoyl, and (AR2)aminosulfonyl; wherein any phenyl group in (TAba) may be optionally substituted with up to three substituents independently selected from (1-4C)alkyl, cyano, trifluoromethyl, nitro, halo, and (1-4C)alkylsulfonyl;

(TAbb) an acetylene of the formula —≡—H or —≡-(1-4C)alkyl;

(TAbc) —X¹—Y¹-AR2, —X¹—Y¹-AR2a, —X¹—Y¹-AR2b, —X¹—Y¹-AR3, —X¹—Y¹-AR3a, or —X¹—Y¹-AR3b;

X¹ is a direct bond or —CH(OH)—; and Y¹ is —(CH₂)_m—, —(CH₂)_n—NH—(CH₂)_m—, —CO—(CH₂)_m—, —CONH—(CH₂)_m—, —C(═S)NH—(CH₂)_m—, or —C(═O)O—(CH₂)_m—; or

X¹ is —(CH₂)_n— or —CH(Me)-(CH₂)_m— and Y¹ is —(CH₂)_m—NH—(CH₂)_m—, —CO—(CH₂)_m—, —CONH—(CH₂)_m—, —C(═S)NH—(CH₂)_m—, —C(═O)O—(CH₂)_m or —S(O)_q—(CH₂)_m—; or

X¹ is —CH₂O—, —CH₂NH—, or —CH₂N((1-4C)alkyl)-; and Y¹ is —CO(CH₂)_m—, —CONH—(CH₂)_m—, or —C(═S)NH—(CH₂)_m—;

with the following provisos; Y¹ is —SO₂— when X¹ is —CH₂NH— or —CH₂N((1-4C)alkyl)-, and

Y¹ is —(CH₂)_m— when X¹ is —CH₂O— or —CH₂N((1-4C)alkyl)-; wherein n is 1, 2, or 3; m is 0, 1, 2, or 3 and q is 0, 1, or 2; and when Y¹ is —(CH₂)_m—NH—(CH₂)_m— each m is independently selected from 0, 1, 2, or 3;

(TB) T is selected from halo, formyl, or —NRv¹Rw¹; or is selected from the following groups: (TBa) R¹⁰CO—, R¹⁰S(O)_q— (q is 0, 1, or 2) or R¹⁰CS—wherein R¹⁰ is selected from the following groups:

(TBaa) -CY1 or CY2;

(TBab) (1-4C)alkoxycarbonyl, trifluoromethyl, —NRvRw, ethenyl, 2-(1-4C)alkylethenyl, 2-cyanoethenyl, 2-cyano-2-((1-4C)alkyl)ethenyl, 2-nitroethenyl, 2-nitro-2-((1-4C)alkyl)ethenyl, 2-((1-4C)alkylaminocarbonyl)ethenyl, 2-((1-4C)alkoxycarbonyl)ethenyl, 2-(AR1)ethenyl, or 2-(AR2)ethenyl; and

(TBac) (1-4C)alkyl {optionally substituted with one or more groups each independently selected from hydroxy, (1-4C)alkoxy, (1-4C)alkanoyl, cyano, halo, trifluoromethyl, (1-4C)alkoxycarbonyl, —NRvRw, (1-6C)alkanoylamino, (1-4C)alkoxycarbonylamino, N-(1-4C)alkyl-N-(1-6C)alkanoylamino, (1-4C)alkylS(O)_q— (q is 0, 1, or 2), CY1, CY2, AR1, (1-4C)alkylS(O)_pNH—, or (1-4C)alkylS(O)_p-((1-4C)alkyl)N— (p is 1 or 2)}; wherein Rv is hydrogen or (1-4C)alkyl; Rw is hydrogen or (1-4C)alkyl; Rv¹ is hydrogen, (1-4C)alkyl, or (3-8C)cycloalkyl; Rw¹ is hydrogen, (1-4C)alkyl, (3-8C)cycloalkyl, formyl, (1-4C)alkyl-CO—, or (1-4C)alkylS(O)_q— (q is 1, or 2);

(TC) T is

wherein in (TC4): n1 is 1 or 2; o1 is 1 or 2, and n1+o1=2 or 3; >A₃-B₃— is >C═C(Rr)-, >C(Rq)-CH(Rr)-, or >N—CH₂—, and G is —O—, —S—, —SO—, —SO₂—, or >N(Rc); Rp is hydrogen, (1-4C)alkyl (other than when such substitution is defined by >A₃-B₃—), hydroxy, (1-4C)alkoxy, or (1-4C)alkanoyloxy;

wherein in (TC4); m1; n1, and o1 are as defined hereinbefore in (TC):

>A₃-B₃— is >N—CH₂—, and G is >C(R¹¹)(R¹²), >C═O, >C—OH, >C—(1-4C)alkoxy, >C═N—OH, >C═N-(1-4C)alkoxy, >C═N—NH-(1-4C)alkyl, >C═N—N((1-4C)alkyl)₂ (the last two (1-4C)alkyl groups above in G being optionally substituted with hydroxy), or >C═N—N—CO-(1-4C)alkoxy;

Rq is hydrogen, hydroxy, halo, (1-4C)alkyl, or (1-4C)alkanoyloxy;

Rr is independently hydrogen or (1-4C)alkyl;

R¹¹ is hydrogen, (1-4C)alkyl, fluoro(1-4C)alkyl, (1-4C)alkyl-thio-(1-4C)alkyl, or hydroxy-(1-4C)alkyl, and R¹² is —[C(Rr)(Rr)]_m2—N(Rr)(Rc) wherein m2 is 0, 1, or 2;

wherein Rc is selected from groups (Rc1) to (Rc5):

(Rc1) (1-6C)alkyl {optionally substituted with one or more (1-4C)alkanoyl groups (including geminal disubstitution) or optionally monosubstituted with cyano, (1-4C)alkoxy,trifluoromethyl, (1-4C)alkoxycarbonyl, phenyl (optionally substituted as AR1), or (1-4C)alkylS(O)_q— (q is 0, 1, or 2); or, on any but the first carbon atom of the (1-6C)alkyl chain, optionally substituted with one or more groups (including geminal disubstitution) each independently selected from hydroxy and fluoro, or optionally monosubstituted with oxo or —NRvRw [wherein Rv is hydrogen or (1-4C)alkyl; Rw is hydrogen, (1-4C)alkyl], (1-6C)alkanoylamino, (1-4C)alkoxycarbonylamino, N-(1-4C)alkyl-N-(1-6C)alkanoylamino, (1-4C)alkylS(O)_pNH—, or (1-4C)alkylS(O)_p-((1-4C)alkyl)N-(p is 1 or 2)};

(Rc2) formyl, R¹³CO—, R¹³SO₂—, or R¹³CS—

wherein R¹³ is selected from (Rc2a) to (Rc2e):

(Rc2a) AR1, AR2, AR2a, AR2b, AR3, AR3a, AR3b, AR4, AR4a, CY1, or CY2;

(Rc2b) (1-4C)alkoxycarbonyl, trifluoromethyl, —NRvRw [wherein Rv is hydrogen or (1-4C)alkyl; Rw is hydrogen or (1-4C)alkyl], ethenyl, 2-(1-4C)alkylethenyl, 2-cyanoethenyl, 2-cyano-2-((1-4C)alkyl)ethenyl, 2-nitroethenyl, 2-nitro-2-((1-4C)alkyl)ethenyl, 2-((1-4C)alkylaminocarbonyl)ethenyl, 2-((1-4C)alkoxycarbonyl)ethenyl, 2-(AR1)ethenyl, 2-(AR2)ethenyl, or 2-(AR2a)ethenyl;

(Rc2c) (1-10C)alkyl {optionally substituted with one or more groups (including geminal disubstitution) each independently selected from hydroxy, (1-10C)alkoxy, (1-4C)alkoxy-(1-4C)alkoxy, (1-4C)alkoxy-(1-4C)alkoxy-(1-4C)alkoxy, (1-4C)alkanoyl, carboxy, phosphoryl [—O—P(O)(OH)₂, and mono- and di-(1-4C)alkoxy derivatives thereof], phophoryl [—O—P(OH)₂ and mono- and di-(1-4C)alkoxy derivatives thereof], and amino; or optionally substituted with one group selected from phosphonate[phosphono, —P(O)(OH)₂, and mono- and di-(1-4C)alkoxy derivatives thereof], phosphinate [—P(OH)₂ and mono- and di-(1-4C)alkoxy derivatives thereof], cyano, halo, trifluoromethyl, (1-4C)alkoxycarbonyl, (1-4C)alkoxy-(1-4C)alkoxycarbonyl, (1-4C)alkoxy-(1-4C)alkoxy-(1-4C)alkoxycarbonyl, (1-4C)alkylamino, di((1-4C)alkyl)amino, (1-6C)alkanoylamino, (1-4C)alkoxycarbonylamino, N-(1-4C)alkyl-N-(1-6C)alkanoylamino, (1-4C)alkylaminocarbonyl, di((1-4C)alkyl)aminocarbonyl, (1-4C)alkylS(O)_pNH—, (1-4C)alkylS(O)_p-((1-4C)alkyl)N—, fluoro(1-4C)alkylS(O)_pNH—, fluoro(1-4C)alkylS(O)_p((1-4C)alkyl)N—, (1-4C)alkylS(O)_q— [the (1-4C)alkyl group of (1-4C)alkylS(O)_q— being optionally substituted with one substituent selected from hydroxy, (1-4C)alkoxy, (1-4C)alkanoyl, phosphoryl [—O—P(O)(OH)₂, and mono- and di-(1-4C)alkoxy derivatives thereof], phophoryl [—O—P(OH)₂ and mono- and di-(1-4C)alkoxy derivatives thereof], amino, cyano, halo, trifluoromethyl, (1-4C)alkoxycarbonyl, (1-4C)alkoxy-(1-4C)alkoxycarbonyl, (1-4C)alkoxy-(1-4C)alkoxy-(1-4C)alkoxycarbonyl, carboxy, (1-4C)alkylamino, di((1-4C)alkyl)amino, (1-6C)alkanoylamino, (1-4C)alkoxycarbonylamino, N-(1-4C)alkyl-N-(1-6C)alkanoylamino, (1-4C)alkylaminocarbonyl, di((1-4C)alkyl)aminocarbonyl, (1-4C)alkylS(O)_pNH—, (1-4C)alkylS(O)_p-((1-4C)alkyl)N—, (1-4C)alkylS(O)_q—, AR1-S(O)_q—, AR2-S(O)_q—, AR3-S(O)_q—, and AR2a, AR2b, AR3a, and AR3b versions of AR2 and AR3 containing groups], CY1, CY2, AR1, AR2, AR3, AR1-O—, AR2-O—, AR3-O—, AR1-S(O)_q—, AR2-S(O)_q—, AR3-S(O)_q—, AR1-NH—, AR2-NH—, AR3-NH— (p is 1 or 2 and q is 0, 1, or 2), and AR2a, AR2b, AR3a, and AR3b versions of AR2 and AR3 containing groups};

(Rc2d) R¹⁴C(O)O(1-6C)alkyl wherein R¹⁴ is AR1, AR2, (1-4C)alkylamino (the (1-4C)alkyl group being optionally substituted with (1-4C)alkoxycarbonyl, carboxy), benzyloxy-(1-4C)alkyl, or (1-10C)alkyl {optionally substituted as defined for (Rc2c)};

(Rc2e) R¹⁵O— wherein R¹⁵ is benzyl, (1-6C)alkyl {optionally substituted as defined for (Rc2c)}, CY1, CY2, or AR2b;

(Rc3) hydrogen, cyano, 2-cyanoethenyl, 2-cyano-2-((1-4C)alkyl)ethenyl, 2-((1-4C)alkylaminocarbonyl)ethenyl, 2-((1-4C)alkoxycarbonyl)ethenyl, 2-nitroethenyl, 2-nitro-2-((1-4C)alkyl)ethenyl, 2-(AR1)ethenyl, 2-(AR2)ethenyl, or (Rc3a)

R¹⁷ is hydrogen (when X⁰⁰ is —NHR¹⁷ or —N(R¹⁷)₂), and

R¹⁷ is (1-4C)alkyl, phenyl, or AR2 (when X⁰⁰ is —OR¹⁷, —SR¹⁷, or —NHR¹⁷); and

R¹⁶ is cyano, nitro, (1-4C)alkylsulfonyl, (4-7C)cycloalkylsulfonyl, phenylsulfonyl, (1-4C)alkanoyl, or (1-4C)alkoxycarbonyl;

(Rc4) trityl, AR1, AR2, AR2a, AR2b, AR3, AR3a, or AR3b;

(Rc5) RdOC(Re)═CH(C═O)—, RfC(═O)C(═O)—, RgN═C(Rh)C(═O)—, or RiNHC(Rj)=CHC(═O)—, wherein Rd is (1-6C)alkyl; Re is hydrogen or (1-6C)alkyl, or Rd and Re together form a (3-4C)alkylene chain; Rf is hydrogen, (1-6C)alkyl, hydroxy(1-6C)alkyl, (1-6C)alkoxy(1-6C)alkyl, —NRvRw [wherein Rv is hydrogen or (1-4C)alkyl; Rw is hydrogen or (1-4C)alkyl], (1-6C)alkoxy, (1-6C)alkoxy(1-6C)alkoxy, hydroxy(2-6C)alkoxy, (1-4C)alkylamino(2-6C)alkoxy, di-(1-4C)alkylamino(2-6C)alkoxy; Rg is (1-6C)alkyl, hydroxy, or (1-6C)alkoxy; Rh is hydrogen or (1-6C)alkyl; Ri is hydrogen, (1-6C)alkyl, AR1, AR2, AR2a, or AR2b, and Rj is hydrogen or (1-6C)alkyl;

wherein

AR1 is an optionally substituted phenyl or optionally substituted naphthyl;

AR2 is an optionally substituted 5- or 6-membered, fully unsaturated monocyclic heteroaryl ring containing up to four heteroatoms independently selected from O, N and S (but not containing any O—O, O—Se or S—S bonds), and linked via a ring carbon atom, or a ring nitrogen atom if the ring is not thereby quaternised;

AR2a is a partially hydrogenated version of AR2, linked via a ring carbon atom or linked via a ring nitrogen atom if the ring is not thereby quaternised;

AR2b is a fully hydrogenated version of AR2, linked via a ring carbon atom or linked via a ring nitrogen atom;

AR3 is an optionally substituted 8-, 9- or 10-membered, fully unsaturated bicyclic heteroaryl ring containing up to four heteroatoms independently selected from O, N, and S (but not containing any O—O, O—S, or S—S bonds), and linked via a ring carbon atom in either of the rings comprising the bicyclic system;

AR3a is a partially hydrogenated version of AR3, linked via a ring carbon atom, or linked via a ring nitrogen atom if the ring is not thereby quaternised, in either of the rings comprising the bicyclic system;

AR3b is a fully hydrogenated version of AR3, linked via a ring carbon atom, or linked via a ring nitrogen atom, in either of the rings comprising the bicyclic system;

AR4 is an optionally substituted 13- or 14-membered, fully unsaturated tricyclic heteroaryl ring containing up to four heteroatoms independently selected from O, N, and S (but not containing any O—O, O—S, or S—S bonds), and linked via a ring carbon atom in any of the rings comprising the tricyclic system;

AR4a is a partially hydrogenated version of AR4, linked via a ring carbon atom, or linked via a ring nitrogen atom if the ring is not thereby quaternised, in any of the rings comprising the tricyclic system;

CY1 is an optionally substituted cyclobutyl, cyclopentyl, or cyclohexyl ring;

CY2 is an optionally substituted cyclopentenyl or cyclohexenyl ring;

wherein; optional substituents on AR1, AR2, AR2a, AR2b, AR3, AR3a, AR3b, AR4, AR4a, CY1, and CY2 are (on an available carbon atom) up to three substituents independently selected from (1-4C)alkyl {optionally substituted with substituents selected independently from hydroxy, trifluoromethyl, (1-4C)alkyl S(O)_q— (q is 0, 1, or 2), (1-4C)alkoxy, (1-4C)alkoxycarbonyl, cyano, nitro, (1-4C)alkanoylamino, —CONRvRw or —NRvRw}, trifluoromethyl, hydroxy, halo, nitro, cyano, thiol, (1-4C)alkoxy, (1-4C)alkanoyloxy, dimethylaminomethyleneaminocarbonyl, di(N-(1-4C)alkyl)aminomethylimino, carboxy, (1-4C)alkoxycarbonyl, (1-4C)alkanoyl, (1-4C)alkylSO₂amino, (2-4C)alkenyl {optionally substituted with carboxy or (1-4C)alkoxycarbonyl}, (2-4C)alkynyl, (1-4C)alkanoylamino, oxo (═O), thioxo (═S), (1-4C)alkanoylamino {the (1-4C)alkanoyl group being optionally substituted with hydroxy}, (1-4C)alkyl S(O)_q— (q is 0, 1, or 2) {the (1-4C)alkyl group being optionally substituted with one or more groups independently selected from cyano, hydroxy and (1-4C)alkoxy}, —CONRvRw, or —NRvRw [wherein Rv is hydrogen or (1-4C)alkyl; Rw is hydrogen or (1-4C)alkyl];

and further optional substituents on AR1, AR2, AR2a, AR2b, AR3, AR3a, AR3b, AR4, AR4a, CY1, CY2 (on an available carbon atom), and alkyl groups (unless indicated otherwise) are up to three substituents independently selected from trifluoromethoxy, benzoylamino, benzoyl, phenyl {optionally substituted with up to three substituents independently selected from halo, (1-4C)alkoxy or cyano}, furan, pyrrole, pyrazole, imidazole, triazole, pyrimidine, pyridazine, pyridine, isoxazole, oxazole, isothiazole, thiazole, thiophene, hydroxyimino(1-4C)alkyl, (1-4C)alkoxyimino(1-4C)alkyl, halo-(1-4C)alkyl, (1-4C)alkanesulfonamido, or —SO₂NRvRw [wherein Rv is hydrogen or (1-4C)alkyl; Rw is hydrogen or (1-4C)alkyl]; and optional substituents on AR2, AR2a, AR2b, AR3, AR3a, AR3b, AR4, and AR4a are (on an available nitrogen atom, where such substitution does not result in quaternization) (1-4C)alkyl, (1-4C)alkanoyl {wherein the (1-4C)alkyl and (1-4C)alkanoyl groups are optionally substituted with substituents independently selected from cyano, hydroxy, nitro, trifluoromethyl, (1-4C)alkyl S(O)_q— (q is 0, 1, or 2), (1-4C)alkoxy, (1-4C)alkoxycarbonyl, (1-4C)alkanoylamino, —CONRvRw, or —NRvRw [wherein Rv is hydrogen or (1-4C)alkyl; Rw is hydrogen or (1-4C)alkyl]}, (2-4C)alkenyl, (2-4C)alkynyl, (1-4C)alkoxycarbonyl, or oxo (to form an N-oxide).