Three models of gynodioecy and androdioecy are presented where males and females are monogenically inherited and may be maintained by having greater pollen or ovule fertility than hermaphrodites or by overdominance at the sex-control loci. Fitnesses of males and hermaphrodites, defined as number of offspring per individual, are frequency-dependent and depend also on the constant selection values. In the absence of over-dominance the fitnesses of unisexual forms in equilibrium populations equal those of the hermaphrodites. Fitness and equilibrium proportions of males in androdioecious populations are less than those of females in gynodioecious populations, with equivalent selection and outcrossing parameters when hermaphrodites may self. The situation where monogenic recessive gynodioecy is combined with monogenic dominant androdioecy to give a digenic model is examined in detail. Recessive gene m for male sterility and dominant gene F for female sterility result in three male, one female, two hermaphrodite and one neuter genotype. There may be overdominance at the male-sterility locus while ovules of females and pollen of males may differ in fertility from ovules or pollen of hermaphrodites. Transition equations for genotype frequencies allow bounds to be put on phenotype frequencies and confirm that dioecy can only evolve if there is complete linkage between sterility mutants when equal proportions of MF/mf male and mf/mf female genotypes are present. Considerable selection differentials are required for evolution of dioecy, especially in more inbred populations. Numerical results indicate that even with free recombination males and females can sometimes be maintained with selection differentials which are insufficient to maintain each unisexual type in the absence of the other. Equilibrium proportions of males and females increase with reduced recombination. Neuters and Mf/mF males are lost when there is no recombination as are MMFf males and hermaphrodites in those cases where dioecy evolves. Fitness values of males and hermaphrodites are again frequency-dependent although selective values are constant. In equilibrium populations fitness of males decreases and that of females increases relative to fitness of hermaphrodites, with reduced recombination. This trend holds therefore during the evolution of dioecy when male and female fitnesses become equal. The mean population fitness generally increases with outcrossing, and also with reduced recombination during evolution of dioecy. When the outcrossing rate for ovules of hermaphrodites, t1, is less than one, the outcrossing rate for their pollen, t2, is greater than t1 in gynodioecious populations, but decreases with the introduction of males when it is sometimes less than t1. The mean outcrossing rate for all pollen and ovules of the population, t3, increases constantly during the evolution of dioecy. Consideration of these and other results leads to a multilocus hypothesis for the evolution of dioecy.