The present invention provides a novel, single-stranded DNA probe which comprises an anti-target segment, a strand of a promoter, and a reporter segment, arranged so that a target segment, which has a 3'-hydroxyl at its terminus, can prime DNA polymerase-catalyzed extension of the target segment along the probe as template, when the target segment is hybridized to the anti-target segment of the probe, to provide an extension product from which transcripts, with the sequence complementary to that of the reporter segment of the probe, can be made by transcription from the promoter corresponding to the promoter segment of the probe. The transcripts, optionally after further amplification or other processing, can be detected. In one embodiment of the invention, the transcripts will be autocatalytically replicatable by an RNA replicase such as Q.beta. replicase. The invention also provides methods of using a probe of the invention in testing a sample of nucleic acid for the presence of a nucleic acid which comprises target segment corresponding to the anti-target segment of the probe and test kits for carrying out such methods with a probe of the invention.