The SgrAI endonuclease displays its maximal activity on DNA with two copies of its recognition sequence, cleaving both sites concertedly. While most restriction enzymes that act concurrently at two sites are tetramers, SgrAI is a dimer in solution. Its reaction at two cognate sites involves the association of two DNA-bound dimers. SgrAI can also bridge cognate and secondary sites, the latter being certain sequences that differ from the cognate by one base-pair. The mechanisms for cognate-cognate and cognate-secondary communications were examined for sites in the following topological relationships: in cis, on plasmids with two sites in a single DNA molecule; on catenanes containing two interlinked rings of DNA with one site in each ring; and in trans, on oligoduplexes carrying either a single site or the DNA termini generated by SgrAI. Both cognate-cognate and cognate-secondary interactions occur through 3-D space and not by 1-D tracking along the DNA. Both sorts of communication arise more readily when the sites are tethered to each other, either in cis on the same molecule of DNA or by the interlinking of catenane rings, than when released from the tether. However, the dimer bound to an oligoduplex carrying either a cognate or a secondary site could be activated to cleave that duplex by interacting with a second dimer bound to the recognition site, provided both duplexes are at least 30 base-pairs long: the second dimer could alternatively be bound to the two duplexes that correspond to the products of DNA cleavage by SgrAI.