The present invention is directed to methods of generating a signal indicative of the presence of a target nucleic acid in a sample by forming a cleavage structure comprising duplex and single-stranded nucleic acid by incubating a sample comprising a target nucleic acid with a thermostable nucleic acid polymerase substantially lacking 5' to 3' exonuclease activity and cleaving said cleavage structure with a thermostable Fen nuclease lacking 5' to 3' synthetic activity to generate a signal.