The macroscopic states of two model systems are specified at two times and their approach to equilibrium for intervening times is studied. The models are the Kac ring and a certain automorphism on the torus. If the relaxation time is short compared to the interval for the boundary value problem, the systems are seen by explicit calculation to decay away from the initial state almost as if the final conditions had not been specified. As the systems approach the final time they exhibit normal decay in the reversed time variable. For longer relaxation times acausal effects may be observed. Some remarks are also included on experimental searches for the acausal effects of future boundary conditions.