Data were collected from 489 progeny. They represented   purebred, F₁, backcross and F₂ inter se combinations of New Zealand White (NN) and Californian (CC) rabbits. They were used to estimate average individual, maternal genetic effects, individual & maternal heterosis and dominance & epistatic genetic effects. The rabbits were produced over 2-year period at Maryout Research Station. Three different genetic models, being Dickerson (1973), Kinghorn (1980) and Koch et al (1985)  were used to estimate crossbreeding parameters.Coefficients of additive breed, heterosis, dominance maternal and recombination loss (epistatic) were discussed. The differences among eight genetic groups were significant for postweaning traits. F_2N had the highest weights (2009.2 g) and daily postweaning gain (32.9 g ) when NC was the terminal sire and when reared by CN dam. Californian had significantly higher postweaning market weight (1957 g by 72 day of age) than (NN) purebred. Significant differences between generations in (F₁ vs. F₂) and (F₂ vs. `P) in weaning weight was found. No difference in postweaning weight could be observed between (NN) and (CC) purebreds. Sex linkage had negative effect for weaning weights. It also had positive effects for postweaning and weights gain. The individual breed effects (A^I) for W54, W72 and postweaning weights gain that were estimated by both genetic models of Dickerson and Kinghorn were positive, while weights from weaning to day 45 postweaning were negative. Average maternal effects (M^I) that were estimated by Dickerson and Kinghorn models had positive effect for early growth traits until weaning weight. However, the weights during postweaning period until 72 days of age or individual daily gain had been negatively effected. Individual dominance (d^I) had positive effect on weaning weight and negative effect on postweaning and weights gain. Additive x additive epistatic effects (gg^I) for the Koch model were significant. They were large and negative for postweaning weight. It was not significantly positive only for weaning weight. In contrast,  the epistatic loss effects (e^I_x) that were estimated by Kinghorn model were significant and had positive effect on postweaning and weights gain. They had negative effect on weaning weight.