The theory of selection on multivariate traits in age-structured populations has important implications for empirical and theoretical studies of life-history evolution. A model of natural selection on a set of correlated quantitative traits with age structure is derived here, using an extension of previous work on selection at a single locus. This formulation provides an equation for the change of the mean of a vector of traits that is accurate is selection is weak, and does not require the population always to be in demographic equilibrium as selection proceeds. The treatment is extended to density-dependent populations, and to equilibrium populations under frequency-dependent selection. In addition, further approximations are derived that produce evolutionary equilibria equivalent to those predicted by optimization and evolutionarily stable strategy (ESS) theory. It is shown that the conditions for equilibrium are valid even if selection is strong.