We studied the dynamics of site-specific recombination by the resolvase encoded by the Escherichia coli transposon Tn3. The pure enzyme recombined supercoiled plasmids containing two directly repeated recombination sites, called res sites. Resolvase is the first strictly site-specific topoisomerase. It relaxed only plasmids containing directly repeated res sites; substrates with zero, one or two inverted sites were inert. Even when the proximity of res sites was ensured by catenation of plasmids with a single site, neither relaxation nor recombination occurred. The two circular products of recombination were catenanes interlinked only once. These properties of resolvase require that the path of the DNA between res sites be clearly defined and that strand exchange occur with a unique geometry. A model in which one subunit of a dimeric resolvase is bound at one res site, while the other searches along adjacent DNA until it encounters the second site, would account for the ability of resolvase to distinguish intramolecular from intermolecular sites, to sense the relative orientation of sites and to produce singly interlinked catenanes. Because resolvase is a type 1 topoisomerase, we infer that it makes the required duplex bDNA breaks of recombination one strand at a time.