Several genotype-by-environment stability measures are in use, but little information exists about their inheritance or genetic inter-relationships. Among those measures in common use are the linear regression coefficient (b), deviations from regression (Sb), coefficient of determination (R2), coefficient of phenotypic variation (CPV) and, more recently, interaction principal components (IPCA) of the additive-main-effect-and-multiplicative-interaction (AMMI) model. Because of the factorial structure of the data, the diallel cross is well suited to study these parameters and their relationship to quantitative traits. For this study a complete diallel cross, derived by mating eight lines from a broad based bread wheat breeding population, was grown for several growing seasons at two Ugandan locations, one of which was prone to yellow rust. Stability parameters and grain yield were measured for each cross. CPV had the highest narrow-sense heritability (h2=0.522) followed by IPCA1 of the AMMI (h2=0.461). Lowest narrow-sense heritabilities were calculated for b and R2 (h2=0.150 and 0.100 respectively). There were high additive genetic correlations (rA) between grain yield and CPV (rA=-0.933), grain yield and IPCA1 (rA=0.707), and grain yield and IPCA2 (rA=0.751). The genetic association between CPV and IPCA1 was also high and negative (rA= -0.934). These results suggest that it may be possible to select simultaneously for high and stable grain yield in this broad-based bread wheat breeding pool by selecting outyielders that exhibit a low CPV.