This paper considers Markov error-correction (MEC) models in which deviations from the long-run equilibrium are characterized by different rates of adjustment. To motivate our analysis and illustrate the various issues involved, our discussion is structured around the analysis of the long-run properties of US stock prices and dividends. It is shown that the MEC model is flexible enough to account for situations where deviations from the long-run equilibrium are nonstationary in one of the states of nature and allows us to test for such a possibility. An empirical specification procedure to establish the existence of MEC adjustment in practice is also presented. This is based on a multi-step test procedure that exploits the differences between the global and local characteristics of systems with MEC adjustment.