The steps of normal bacterial conjugation (union, transfer, integration and segregation) are described in analytical terms. Only two parameters are utilized: nu(mt) (0), the probability of interruption of transfer of the male chromosome per unit chromosomal distance; and nu(r) (0), the probability per unit chromosomal distance of a recombinational event. Experimentally these two parameters have the same value (0.06 min(-1) or 10(-6) per nucleotide pair). Irradiation of the donor parent prior to mating increases the transfer parameter (nu(mt) = nu(mt) (0) + sigma(mt)D) and a complete description of the radiation response of recombinant production is obtained by a consideration of the single parameter sigma(mt). Irradiation of the recipient parent prior to mating increases the recombination parameter (nu(r) = nu(r) (0) + sigma(r)D) and a complete description of the radiation response of recombinant production is obtained by the addition of the parameter sigma(r). Experimentally sigma(mt) and sigma(r) are found to have the same value, approximately 0.004 krad(-1) min(-1) for X-irradiation. It is thus possible to describe mathematically the behavior of the unperturbed mating system by a single parameter nu(0); a single additional parameter sigma is adequate to describe the behavior of the system when either parental type is irradiated prior to mating. The unexpected observation that nu(mt) and nu(r) have the same value suggests that common molecular mechanisms are involved in the transfer and integration steps.