Bivariate analyses of functional longevity in dairy cattle measured as survival to next lactation (SURV) with milk yield and fertility traits were carried out. A sequential threshold-linear censored model was implemented for the analyses of SURV. Records on 96 642 lactations from 41 170 cows were used to estimate genetic parameters, using animal models, for longevity, 305 d-standardized milk production (MY305), days open (DO) and number of inseminations to conception (INS) in the Spanish Holstein population; 31% and 30% of lactations were censored for DO and INS, respectively. Heritability estimates for SURV and MY305 were 0.11 and 0.27 respectively; while heritability estimates for fertility traits were lower (0.07 for DO and 0.03 for INS). Antagonist genetic correlations were estimated between SURV and fertility (-0.78 and -0.54 for DO and INS, respectively) or production (-0.53 for MY305), suggesting reduced functional longevity with impaired fertility and increased milk production. Longer days open seems to affect survival more than increased INS. Also, high productive cows were more problematic, less functional and more liable to being culled. The results suggest that the sequential threshold model is a method that might be considered at evaluating genetic relationship between discrete-time survival and other traits, due to its flexibility.