The extent of amino acid differences of major histocompatibility complex molecules within species is unusually high, consistent with the finding that some pairs of alleles have persisted for more than ten million years and the view that the polymorphism has been maintained by natural selection. The disparity between synonymous and non-synonymous substitutions in the antigen recognition site, however, suggests that some non-synonymous sites have undergone a number of substitutions whereas others have little or none. To describe statistically such an overdispersed underlying process, commonly used Poisson processes are inadequate. An alternative process leads to the surprising conclusion that each non-synonymous site has accumulated as many as 2.6 substitutions, on the average, in the two lineages leading to humans and mice. The standard deviation is also very large (6.6) and the dispersion index (the ratio of the variance to the mean) is at least 17. The substitution process thus inferred qualitatively agrees with the disposition (a boomerang pattern) of substitutions between HLA-A2 and Aw68 alleles, and quantitatively agrees well with that expected where the evolution of major histocompatibility complex molecules has long been driven mostly by balancing selection.