S1 nuclease, the single-strand specific nuclease from Aspergillus oryzae can cleave both strands of circular covalently closed, superhelical simian virus 40 (SV40) DNA to generate unit length linear duplex molecules with intact single strands. But circular, covalently closed, nonsuperhelical DNA, as well as linear duplex molecules, are relatively resistant to attack by the enzyme. These findings indicate that unpaired or weakly hydrogen-bonded regions, sensitive to the single strand-specific nuclease, occur or can be induced in superhelical DNA. Nicked, circular SV40 DNA can be cleaved on the opposite strand at or near the nick to yield linear molecules. S1 nuclease may be a useful reagent for cleaving DNAs at regions containing single-strand nicks. Unlike the restriction endonucleases, S1 nuclease probably does not cleave SV40 DNA at a specific nucleotide sequence. Rather, the sites of cleavage occur within regions that are readily denaturable in a topologically constrained superhelical molecule. At moderate salt concentrations (75 mM) SV40 DNA is cleaved once, most often within either one of the two following regions: the segments defined as 0.15 to 0.25 and 0.45 to 0.55 SV40 fractional length, clockwise, from the EcoRI restriction endonuclease cleavage site (defined as the zero position on the SV40 DNA map). In higher salt (250 mM) cleavage occurs preferentially within the 0.45 to 0.55 segment of the map.