DNA winds about itself in a right-handed or left-handed fashion at several structural levels. The double helix is generally right-handed and is given a (+) sign by convention, whereas supercoiling of the helix axis is always (-) in the cell. The winding in higher -order forms such as knots and catenanes is unknown, and this has impeded elucidation of the mechanisms of their formation and resolution by replication, recombination and topoisomerase action. We introduce here a procedure for determining the handedness of DNA winding by inspection of electron micrographs of DNA molecules coated with Escherichia coli RecA protein. We demonstrate the validity of the method and show that DNA topoisomerase I of E. coli generates an equal mixture of (+) and (-) duplex DNA knots, and that one product of recombination by resolvase of transposon Tn3 (refs 8, 9) is a catenane of uniquely (+) sign.