SUMMARYGenetic parameters for visual assessment traits measured at 487 days of age (body structure (BS), finishing precocity (FP) and muscling (MS)), body weight at 450 days of age (W450), age at first calving (AFC), heifer pregnancy (HP) and stayability (STAY, i.e. the probability of a cow to produce at least three calves before reaching 76 months of age) were estimated in Nellore cattle, seeking to include these traits in the selection criteria for dams. The statistical models included additive genetic and residual random effects using single- and two-trait Bayesian analyses. The average heritability estimates were equal to 0·37 for BS, 0·42 for FP, 0·37 for MS and 0·48 for W450. Age at first calving had a low average heritability estimate (0·13), while HP and STAY estimates were higher (0·36 and 0·24, respectively). The genetic correlations between AFC, HP and STAY with visual assessment traits and body weight were favourable, indicating that selecting animals with higher BS, FP, MS and W450 values will result in the indirect selection of animals with lower AFC and successful scores for HP and STAY. The selection of heifers that present an early pregnancy should anticipate AFC and improve HP in the current herd. Except for AFC, the heritability and genetic correlation estimates between the studied traits justify their inclusion in the selection criteria of the Nellore breeding programme.