Learning is introduced into a sequence of large square endowment economies indexed by n, in which agents live n periods. Young agents need to forecast n - 1 periods ahead in these models in order to make consumption decisions, and thus these models constitute multi-step ahead systems. Real time learning is introduced via least squares. The systems studied in this paper are sometimes locally convergent when n = 2,3 but are never locally convergent when . Because the economies studied are analogous, nonconvergence can be attributed solely to the multi-step ahead nature of the forecast problem faced by the agents. We interpret this result as suggesting that beliefs-outcomes interaction may be an important element in explaining actual dynamics in general equilibrium systems of this type.