An asynchronous thermal cycling protocol for nucleic acid amplification uses two primers with thermal melting temperatures different by about 10 to 30° C. After the higher melting primer has annealed and polymerase mediated extension, the uncopied, single-stranded target sequence may be hybridized and detected by a probe. DNA probes may be cleaved by the exonuclease activity of a polymerase. The probe may be a non-cleaving analog such as PNA. When a probe is labelled with a reporter dye and a quencher selected to undergo energy transfer, e.g. FRET, fluorescence from the reporter dye may be effectively quenched when the probe is unbound. Upon hybridization of the probe to complementary target or upon cleavage while bound to target, the reporter dye is no longer quenched, resulting in a detectable amount of fluorescence. The second, lower-melting primer may be annealed and extended to generate a double-stranded nucleic acid. Amplification may be monitored in real time, including each cycle, or at the end point. The asynchronous PCR thermal cycling protocol can generate a preponderance of the PCR amplicon in single-stranded form by repetition at the end of the protocol of annealing and extension of the higher melting primer.