During site-specific DMA recombination, which brings about genetic rearrangement in processes such as viral integration and excision and chromosomal segregation, recombinase enzymes recognize specific DNA sequences and catalyse the reciprocal exchange of DNA strands between these sites. The bacteriophage recombinase Cre catalyses site-specific recombination between two 34-base-pair loxP sites. The crystal structure at 2.4 Angstrom resolution of Cre bound to aloxP substrate reveals an intermediate in the recombination reaction, fin which a Cre molecule has cleaved the substrate to form a covalent 3’-phosphotyrosine linkage with the DNA. Four recombinases and two loxP sites form a synapsed structure in which the DNA resembles models of four-way Holliday-junction intermediates. The Cre-loxP complex challenges models of site-specific recombination that require large changes in quaternary structure. Subtle allosteric changes at the carboxy termini of the Cre subunits may instead coordinate the cleavage and strand-exchange reactions.