Abstract The frequency of homologous recombination is believed to be a linear function of the length (N bp) of homology between DNAs. Here, the N intercept is believed to be determined by a threshold length below which some physical constraint is effective. In the mammalian gene targeting systems, however, the frequency depends more steeply than linearly on the homology length. To explain both the linear dependence and the steeper dependence, we propose a model where the branch point of a reaction intermediate is assumed to "walk randomly" along the homologous region until it is processed. The intermediate is assumed to be destroyed if the branch point ever reaches either end of the homology. In this model, the length dependence is governed by a parameter, h, which is defined as efficiency of processing of the intermediate and reflects unlikelihood of the destruction at either end of the homology. We find that the frequency is proportional to N3 for smaller N and is a linear function of N for larger N. Where the shift from the N3 dependence to the linear dependence takes place is determined by the parameter h. The range of N showing the N3 dependence becomes narrower as h becomes larger. The dependence steeper than linear dependence, which is observed not only in the mammalian gene targeting system but also in bacteriophage T4, Escherichia coli and yeast systems, agrees well with the predicted N3 dependence. The N intercept is determined not by physical (or structural) constraints but only by the parameter h in this model.