Combining ability studies for grain yield and its primary component traits in diallel crosses involving seven diverse wheat cultivars of bread wheat (Triticum aestivum L.) over generations F1-F5 are reported. The general and specific combining ability variances were significant in all generations for all the traits except specific combining ability variance for number of spikes per plant in the F5. The ratio of general to specific combining ability variances was significant for all the traits except grain yield in all the generations. This indicated an equal role of additive and non-additive gene effects in the inheritance of grain yield, and the predominance of the former for its component traits. The presence of significant specific combining ability variances in even the advanced generations may be the result of an additive x additive type of epistasis or evolutionary divergence among progenies in the same parental array. The relative breeding values of the parental varieties, as indicated by their general combining ability effects, did not vary much over the generations. The cheap and reliable procedure observed for making the choice of parents, selecting hybrids and predicting advanced generation (F5) bulk hybrid performance was the determination of breeding values of the parents on the relative performance of their F2 progeny bulks.