SummaryA model which takes account of heterosis for total seed yield and autofertility was used to trace the evolution of the expected average inbreeding coefficient (F) of a synthetic variety of field beans under multiplication. In every case, the value of F rapidly approached an equilibrium value which depended largely on the amount of cross-fertilization and very little on the higher seed total set or amount of selfing on less inbred plants. There was no indication of any fluctuation in F from generation to generation when the proportion of cross-fertilization was constant. The possibility of reducing the coefficients of inbreeding of generations likely to be used on the farm (syn-4 and later) by hand pollination instead of open pollination of the parents and by promoting cross-pollination by artificial increases in numbers of bees or adjustment of environmental factors during multiplication were examined. Although the method of parental pollination had little effect, induced increases in bee activity led to significant reductions in F when the ambient frequency of bee pollinations was low. The generation at which this procedure gave the maximum effect was the final generation of seed increase (syn-3), but an alternative would be for farmers to use bees on the first commercial crop. In any case, only seed from crops with adequate bee pollination should be used to sow commercial crops.As the breeding system was shown to be effectively very similar to one in which all plants are equally self-fertile, it should be possible to take account of the number (n) and coefficients of inbreeding (F0) and interrelationship (r0) of the parents, and to predict the yield of advanced generations using formulae given by Busbice (1969, 1970).