parental, f1, f2, bc1 and bc2 generations of four crosses involving four cultivars of durum wheat (triticum durum desf.) were evaluated at two sites in tunisia. a three-parameter model was found inadequate for all cases except crosses chili x cocorit 71 at site sidi thabet and inrat 69 x karim at both sites. in most cases a digenic epistatic model was sufficient to explain variation in generation means. dominance effects (h) and additive x additive epistasis (i) (when significant) were more important than additive (d) effects and other epistatic components. considering the genotype-by-environment interaction, the non-interactive model (m, d, h, e) was found adequate. additive variance was higher than environmental variance in three crosses at both sites. the estimated values of narrow-sense heritability were dependent upon the cross and the sites and were 0%-85%. the results indicate that appropriate choice of environment and selection in later generations would increase grain protein content in durum wheat.