When the recA protein (RecA) of Escherichia coli promotes strand exchange between single-stranded DNA (ssDNA) circles and linear double-stranded DNAs (dsDNA) with complementary 5' or 3' ends a polarity is observed. This property of RecA depends on ATP hydrolysis and the ssDNA that is displaced in the reaction since no polarity is observed in the presence of the non-hydrolyzable ATP analog, ATP gamma S, or in the presence of single-strand specific exonucleases. Based on these results a model is presented in which both the 5' and 3' complementary ends of the linear dsDNA initiate pairing with the ssDNA circle but only one end remains stably paired. According to this model, the association/dissociation of RecA in the 5' to 3' direction on the displaced strand determines the polarity of strand exchange by favoring or blocking its reinvasion into the newly formed dsDNA. Reinvasion is favored when the displaced strand is coated with RecA whereas it is blocked when it lacks RecA, remains covered by single-stranded DNA binding protein or is removed by a single-strand specific exonuclease. The requirement for ATP hydrolysis is explained if the binding of RecA to the displaced strand occurs via the dissociation and/or transfer of RecA, two functions that depend on ATP hydrolysis. The energy for strand exchange derives from the higher binding constant of RecA for the newly formed dsDNA as compared with that for ssDNA and not from ATP hydrolysis.