A Bayesian model for quantitative genetic analysis of longitudinaltraits is presented. It connects the model known as the Kalmanfilter (KF) with the standard mixed model of quantitative genetics.The KF model can be implemented easily in a Bayesian frameworkbecause, under standard prior assumptions, all fully conditionalposterior distributions have closed forms. An analysis of beefcattle growth data including comparisons with a standard multivariatemodel was performed to assess applicability of the KF to animalbreeding. Models were compared using the deviance informationcriterion and the Bayes factor. Models in which a KF acted onadditive genetic and maternal effects were favored by the devianceinformation criterion, although KF did not describe residual(co)variance adequately. The Bayes factor did not provide conclusiveevidence in favor of a specific model. Fitting KF to longitudinaltraits provides estimates of genetic value for a whole rangeof time points, assuming that there are genetic differencesthrough time between and within individuals. Different modelsembedding the KF in a mixed model were demonstrated to providea more parsimonious (co)variance structure than a standard multitraitspecification for the quantitative genetic analysis of longitudinaldata.