Building on Preston and Campbell's two-sex model of intergenerational transmission, this article provides a theoretical analysis of the dynamics of the racial distribution in black-white-mulatto systems. The author shows that "bounded" patterns of racial classification and switching imply long-run racial homogeneity in the absence of differential reproduction. Beyond the theoretical analysis, the author attempts to account for the dramatic growth of the white population share in Puerto Rico in the early 20th century. Because the effects of racial classification and differential reproduction were roughly offsetting, the observed growth of the white share can be attributed almost entirely to racial switching.