The open population Cormack-Jolly-Seber (CJS) capture–mark–recapture model for estimating survival allows for random temporary emigration from the sampling area, but Markovian temporary emigration can bias estimates of survival. We explore a multistate capture–recapture model that has been proposed for coping with Markovian temporary emigration. We provide a comprehensive assessment of the performance of this model using computer algebra and simulation. We found that most model parameters were identifiable unless survival, emigration, and immigration were all time dependent. Simulation results showed that intrinsically identifiable parameters were estimated without bias and that precision of survival estimates was always high. When temporary emigration was Markovian, precision of estimates of emigration, immigration, and recapture probabilities was acceptable; otherwise it was not. Test component 2.Ct of the goodness-of-fit test for the CJS model had good power to detect Markovian temporary emigration. We conclude that the multistate model works well when temporary emigration is Markovian (i.e., when the CJS model should not be used) and when survival and recapture probabilities are high.