RESUMOMilk production from each State was considered as a different trait and variances were assumed heterogeneous. Milk production was also analyzed using a single-trait model assuming homogeneity of variance. (Co)variance components and genetic parameters were estimated by Bayesian inference, via Gibbs sampler (GS), using a model which included season of calving, genetic group, herd-year of calving and parity as fixed effects and animal additive genetic, permanent environmental and residual as random effects. Convergence of the GS chain to the stationary distribution was diagnosed using the method described by Heidelberg & Welch (1983). The posterior precision of the variance components and the heritability were high in the singletrait analysis. Posterior mean and standard deviation (SD) of heritability of milk yield were 0,278±0,012. For the multipletrait analysis, posterior precisions of the (co)variance components were larger for SP and PR states. Posterior means and standard errors of heritability for MG, SP, PR, SC, and RS were 0.280±0.021, 0.233±0.015, 0.280±0.012, 0.393±0.026, and 0.382±0.022, respectively. Genetic correlations for milk yield between the five states were very low and ranged from 0.070 to 0.364, suggesting the presence of genotype by environment interaction. Differences in genetic and residual variances of milk yield among the states indicate it would be necessary to account for heterogeneous variances in genetic evaluations.