A Bayesian analysis via Markov chain Monte Carlo methods extending the simultaneous and recursive model of Gianola and Sorensen (2004) was proposed to account for possible population heterogeneity. The method was used to infer relationships between milk yield and somatic cell scores of Norwegian Red cows. Data consisted of test-day records of milk yield and somatic cell score of first-lactation cows during the first 120 d of lactation. Results suggested large negative direct effects from somatic cell score to milk yield and small reciprocal effects from milk yield to somatic cell score. The direct effects were larger in the first 60 d of lactation than in the subsequent period. Bayesian model selection strongly favored the simultaneous and recursive models for milk yield and somatic cell score over the corresponding mixed model without considering simultaneity or recursiveness. Estimated effects between milk yield and somatic cell score seemed to be yield-dependent, larger in higher producing cows than in lower producing cows. Heritability estimates from the simultaneous and recursive models were similar to those from the mixed model, but some genetic correlations differed considerably among models.