Simultaneous analysis of correlated traits that change with time is an important issue in genetic analyses. Several methodologies have already been proposed for the genetic analysis of longitudinal data on single traits, in particular random regression and character process models. Although the latter proved, in most cases, to compare favourably to alternative approaches for analysis of single function-valued traits, they do not allow a straightforward extension to the multivariate case. In this paper, another methodology (structured antedependence models) is proposed, and methods are derived for the genetic analysis of two or more correlated function-valued traits. Multivariate analyses are presented of fertility and mortality in Drosophila and of milk, fat and protein yields in dairy cattle. These models offer a substantial flexibility for the correlation structure, even in the case of complex non-stationary patterns, and perform better than multivariate random regression models, with fewer parameters.