Mating designs are useful to estimate genetic variability of some population. Depending on the complexity and combination of mating designs used, different components of the total genetic variation can be estimated. Using the Design III (Comstock and Robinson, 1952), Triple Testcross (Kearsey and Jinks, 1968), S1 progenies, and information from the Analysis of Covariance of S1 and Half-sib family means, Wolf (1995) tested for the significance of epistatic effects and the importance of epistatic variances compared with the additive and dominance variances of an F2 reference population developed from the cross of two maize (Zea mays L.) inbred lines, B73 and Mo17. Wolf (1995) assumed that the results derived by Bradshaw (1983) on the genetic covariance between half-sib and S1 progeny means could be applied for his study. However, the structures of the populations used by Bradshaw (1983) and Wolf (1995) to derive the genetic components of variance were not exactly the same. The main objective of this study was to verify if Wolf (1995) could have applied the results from Bradshaw (1983). For the case of a model that included digenic epistatic variances Wolf (1995) considered COV(half-sib,S1) = 12s2A +14s2A A with the half-sib families (represented by HSt) obtained as the average of the three testcross families (F2 x P 1, F2 x P2 and F2 x F 1), instead of half-sib families (represented by HSp) obtained by using the population as the tester (Bradshaw, 1983). Using a different approach (with potential for several other applications in quantitative genetics), we verified that in both mating structures COV(half-sib,S 1) = 12s2A +14s2A A . However, the theoretical values of those covariances in terms of genetic effects for the case of two loci include terms that could be considered as sources of bias when referring to the F2 population. Two conclusions were obtained. First, if epistatic effects involving dominance are disregarded (or negligible) the bias is eliminated. Second, if those epistatic: effects are important, in practice the use of HSp (reference population as tester) would be preferred rather than the use of HSt (average of the three testcrosses). Some practical recommendations and suggestions for future research are considered.