Age-period-cohort (APC) models are frequently used to analyze mortality or morbidity rates stratified by age group and period. For the case in which rates are given in different strata, multivariate APC models have been considered only recently. Such models share a set of parameters, for example, the age effects, while the other parameters may vary across strata. We show that differences of strata-specific effects are identifiable. We then propose a Bayesian approach based on smoothing priors to estimate multivariate APC models. This provides an alternative to maximum likelihood (ML) estimates of relative risk in the case of equal intervals and gives useful results even in the case of unequal intervals, where ML estimates have severe artifacts. This is illustrated with data on female mortality in Denmark and Norway and data on chronic obstructive pulmonary disease mortality of males in England and Wales, stratified by 3 different areas: Greater London, conurbations excluding Greater London, and nonconurbation areas.