We examined the effects of cognitive training with elderly participants from the Seattle Longitudinal Study. Subjects were classified as having remained stable or having declined over the previous 14-year interval on each of two primary abilities, spatial orientation and inductive reasoning. Subjects who had declined on one of these abilities received training on that ability; subjects who had declined on both abilities or who had remained stable on both were randomly assigned to the spatial orientation or inductive reasoning training programs. Training outcomes were examined within an ability-measurement framework with empirically determined factorial structure. Significant training effects, at the level of the latent ability constructs, occurred for both spatial orientation and inductive reasoning. These effects were general, in that no significant interactions with decline status or gender were found. Thus, training interventions were effective both in remediating cognitive decline on the target abilities and in improving the performance of stable subjects.