The recent advent of molecular markers has created a great potential for the understanding of quantitative inheritance. In parallel to rapid developments and improvements in molecular marker technologies, biometrical models have been constructed, refined and generalized for the mapping of quantitative trait loci (QTL). However, current models present restricitions in terms of breeding designs to which they apply. In this paper, we develop an approach for the generalization of the mixture model for progeny from a single bi-parental cross of inbred lines. Detailed derivations are given for genetic designs involving populations developed by selfing, i.e., where marker genotypes are obtained from F(x) (x >=2) individuals and where phenotypes are measured on F(y) (y >=x) individuals or families. Extensions to designs involving doubled-haploids, backcross-derived individuals and random matings are outlined. The derivations presented here can easily be combined with current QTL mapping approaches.