a) a reaction vessel;

b) means for maintaining a first reaction region of the reaction vessel at a temperature range suitable for separating double stranded DNA molecules into single stranded DNA molecules,

a second reaction region of the reaction vessel at a temperature range suitable for hybridization of the single stranded DNA molecules with primers that are complementary to specific portions of the single stranded DNA molecules so as to form partially double stranded DNA molecules, and

a third reaction region of the reaction vessel at a temperature range suitable for DNA polymerization reaction of the primers in the partially double stranded DNA molecules so as to generate primer extension products; and

c) means for circulating the DNA molecules through the first, second, and third reaction regions to make amplification of the target DNA sequences occur,

wherein an immobilized DNA polymerase is exclusively positioned in the third reaction region of the reaction vessel and the circulating means circulates the DNA molecules repeatedly at least once; and further wherein the apparatus comprises an opening adapted to receive the reaction vessel and having a closed end defined by the means for maintaining the first reaction region.