Estimates of genetic and phenotypic parameters for body weight, degree of maturity and measures of gain rate on 910 Barki sheep (530 females and 380 males), progeny of 49 unrelated rams were calculated and used to predict the responses to selection both as a result of direct and indirect selection. Weight at 48 months of age was considered the mature weight as it was the last weight taken and was different significantly (P< 0.05) from the preceding weight. The phenotypic and genetic coefficient of the variation in degree of maturity declined with age to zero at maturity. Degree of maturity was more variable than body weight genetically till six months and phenotypically till 14 months when the order was reversed. Heritabilities for degree of maturity were essentially lower than the corresponding heritabilities for body weight. The genetic inter-age correlations for degree of maturity were almost always lower than the corresponding phenotypic correlations. All were positive, so that animals more mature at a given age also tended to be more mature at any later age. High positive correlations were found within the marketing body weight group (W₁₀ and W₁₂), the pre-marketing group (W₀₄, W₀₆ and W₀₈) and the post-marketing group (W₂₄, W₃₆ and W₄₈). The marketing and pre-marketing body weights show essentially high genetic and phenotypic correlations, implying the possibility of selecting heavier animals at marketing by using early information. All measures of average gain rate decline from 4 to 48 months of age. The CV's reached their highest values for average absolute growth rate (AGR_a) and average absolute maturing rate (AMR_a) between 16 and 24 months of age and average relative growth rate (RGR_a) between 36 and 48 months of age.  AGR_a, AMR_a and RGR_a were highly genetically correlated with each other whenever they referred to the same period of gain. Their estimates at the first five age intervals were mostly negatively correlated with their estimates from 36 to 48 months of age. Substantial increase in weight at age of selection and less increase in weight at all other ages would result from selection for body weights and degrees of maturity. Selection for AGR_a, AMR_a and RGR_a at early stages (4 to 8 months) would result in increase in body weight and degree of maturity at all subsequent stages. Selection for AGR_a orAMR_a after 12 months of age would have little effect on mature weight. Increase in mature weight would be expected from animals selected for their lower than average RGR_a after the age of 12 months.