This paper presents an algebraic analysis of the equilibrium reached as a result of the opposition of selection and recombination in a heterostyled population. It is shown that, when the fitness of a selfed progeny is sufficiently small compared with that of outcrossed progeny, the frequencies of the self-fertile recombinant phenotypes can be expected to be of roughly the same order of magnitude as the frequencies of the corresponding crossover events. Data from population surveys suggest that these frequencies must be less than 10-3. These results are also used to discuss the possibility of ordering the component loci of the heterostyly supergene. The breakdown of heterostyly due, for example, to inefficient insect pollination is also investigated. It is shown that the self-fertile homostyle with the dominant allele for pollen type will usually replace heterostyly. This agrees with data on a number of genera containing both heterostyled and secondarily homostyled species.