Genetic parameters were estimated for first lactation survival defined as a binary trait (alive or dead to second calving) and the curve shape traits of milk yield, fat and protein percentages using information from 25 981 primiparous Tunisian Holsteins. For each trait, shape curves (i.e. peak lactation, persistency), level of production adjusted to 305 days in milk (DIMs) for total milk yield (TMY), and average fat (TF %) and protein (TP %) percentages were defined. Variance components were estimated with a linear random regression model under three bivariate animal models. Production traits were modelled by fixed herd × test-day (TD) interaction effects, fixed classes of 25 DIMs × age of calving × season of calving interaction effects, fixed classes of pregnancy, random environment effects and random additive genetic effects. Survival was modelled by fixed herd × year of calving interaction effects and age of calving × season of calving interaction effects, random permanent environment effects, and random additive genetic effects. Heritability (h2) estimates were 0.03 (±0.01) for survival and 0.23 (±0.01), 0.31 (±0.01) and 0.31 (±0.01) for TMY, TF % and TP %, respectively. Genetic correlations between survival and TMY, TF % and TP % were 0.26 (±0.08), −0.24 (±0.06) and −0.13 (±0.06), respectively. Genetic correlations between survival and persistency for fat and protein percentages were −0.35 (±0.09) and −0.19 (±0.09), respectively. Cows that had higher persistencies for fat and protein percentages were more likely not to survive.