Holliday junctions (HJs) are key intermediates in homologous recombination and are especially important for the production of crossover recombinants. Bacterial RecA family proteins promote the formation and branch migration of HJs in vitro by catalysing a reciprocal DNA-strand exchange reaction between two duplex DNA molecules, one of which contains a single-stranded DNA region that is essential for initial nucleoprotein filament formation. This activity has been reported only for prokaryotic RecA family recombinases, although eukaryotic homologues are also essential for HJ production in vivo. Here we show that fission yeast (Rhp51) and human (hRad51) RecA homologues promote duplex-duplex DNA-strand exchange in vitro. As with RecA, a HJ is formed between the two duplex DNA molecules, and reciprocal strand exchange proceeds through branch migration of the HJ. In contrast to RecA, however, strand exchange mediated by eukaryotic recombinases proceeds in the 3'-->5' direction relative to the single-stranded DNA region of the substrate DNA. The opposite polarity of Rhp51 makes it especially suitable for the repair of DNA double-strand breaks, whose repair is initiated at the processed ends of breaks that have protruding 3' termini.