The case-exposure study, described in 1983, is a modification of the case-control study that allows estimation of risk ratios without need for a rare-disease assumption. For a fixed population the approach is the same as the case-base or case-cohort study. Two sampling strategies have been described for extending application of the case-exposure approach to stationary populations, although the validity of the extension was not proven. As shown here, the two sampling strategies for stationary populations can provide valid estimates of the risk ratio, but restrictive assumptions related to stationarity may limit application of the strategy. We also show that the case-exposure study depends on the stationarity assumptions in a different, possibly more restrictive way than some other case-control approaches. We emphasize limitations of the case-exposure study that may preclude its use, particularly it the period of risk is long.