Methods for amplifying target nucleic acid sequences using a nucleic acid polymerase lacking 5 exonuclease activity and a set of oligonucleotide primers. Preferably, a primer array is used. The primer array contains two sets of primers. One set contains at least two complementary primers. The other set contains at least two sense primers. Using the described methods amplification can be carried out under essentially constant environmental conditions without the requirement for exonuclease activity or restriction endonu- clease activity.