Genetic parameters of first lactation survival and curve shape traits of milk yield, fat and protein percentages were estimated using information of 25,981 primiparous Tunisian Holsteins belonging to large herds. For each trait lactation peak, apparent persistency, real persistency and level of production adjusted to 305 days in milk were defined. Variance components were estimated under three bivariate animal models with a linear random regression model. Milk yield as well as fat and protein percentages were modelled by fixed herd × test day interaction effects, fixed classes of 25 days in milk × age of calving × season of calving interaction effects, random environment effects, and random additive genetic effects. Survival was modelled by fixed herd × year of calving interaction effects, age of calving × season of calving interaction effects, random environment permanent effects, and random additive genetic effects. Heritability estimates were 0.03 for survival, 0.23, 0.29 and 0.30 for average milk yield, fat and protein percentages adjusted to 305 days in milk, respectively. Genetic correlations between survival and average milk yield, fat and protein percentages adjusted to 305 days in milk were 0.33, -0.33 and -0.14, respectively. Genetic correlations between survival and real persistency for fat and protein percentages were -0.24 and -0.15, respectively. Cows that had higher persistencies for fat and protein percentages, and therefore flatter fat and protein percentages curves, were more likely not to survive. This was due to higher fat percentages at the end of the lactation leading to the hypothesis that cows producing higher fat percentage dispose of less energy available for gestation and were therefore less likely to be or remain pregnant and, therefore, to survive.