To deal with differences between reciprocal crosses found in many animal breeding experiments, an extension of the general model for genetic effects, given by Eberhart and Gardner (1966, Biometrics 22, 864-881), is presented. In this extension, reciprocal differences between crosses are defined in terms of several maternal and sex-linked parameters, the latter being expressed as functions of gene values and their frequencies. Models are given for several kinds of crosses. Experimental setups or designs of increasing complexity are presented for the estimation of some of the parameters in the models, particularly the sex-linked and maternal ones, as well as the interpopulation heterotic additive-by-additive epistasis. For prediction purposes, different analyses are suggested for the model with highly correlated variables. If the genetic architecture of a trait in different populations is to be compared, the analysis of variance will provide enough degrees of freedom to allow the investigation of the importance of each kind of genetic effect. An example which uses all possible two-way crosses and a partial set of three-way crosses applied to two quantitative traits in the flour beetle, Tribolium castaneum, is included merely as a guide for computations. Population means given by Eberhart and Gardner are extended to incorporate the inbreeding coefficient.