The quantitative investigation of problems in population genetics has mainly been concerned, until recently, with the analysis of gene frequencies at a single locus. Such an approach is natural as a first step, but necessarily requires assumptions about the interaction effects of other loci to be meaningful. Despite the latter restriction a number of important results have been obtained from this approach, to a large extent by the researches of R. A. Fisher and Sewall Wright. Latterly interest has moved to multilocus behavior, and as a first step in this direction the two-locus case has received increasing attention (see, for example, Kimura (1956), Lewontin and Kojima (1960), Bodmer and Parsons (1962), Moran (1964)). Although such an extension from the single locus case still requires assumptions about the interactions of the loci considered with the remaining loci, it is at least possible to treat, for example, the effect of linkage between loci, which would be impossible in a single locus analysis (see in particular Kimura (1956) and Bodmer and Parsons (1962)). In another direction, Moran (1964) has shown that the analogues of several single locus theorems (including Fisher's fundamental theorem of natural selection) are no longer always true in the two locus case. All the investigations referred to above consider deterministic models, a stochastic treatment not having been attempted so far. A notable feature of the deterministic analyses is that close linkage between the loci appears, in all cases considered, to be desirable. An example of this, considered