Type I topoisomerases catalyze topological changes in duplex DNA by reversibly nicking one strand, whereas type II enzymes catalyze the transient breakage of both strands simultaneously. The type I enzymes alter the linking number of covalently closed circular DNA in steps of one, presumably by allowing an unbroken segment of one strand of the DNA to move through the transient single-strand break in the other strand. The type II enzymes alter the linking number in steps of two by allowing an unbroken segment of duplex DNA to pass through the transient double-strand break.