The semi-Markov assumption emphasizes the importance of time spent in a state. In order to compute this type of multistate model, most transition times are always considered to be exactly identified or right censored. However, in the longitudinal analysis of chronic diseases, investigators are often confronted with interval-censored data (transition times are known to have occurred in some interval). Thus, the two key issues are the modeling of the duration dependence and the interval censoring. In this article, we define a semi-Markov model, allowing for interval censoring, for parametric hazard functions with a ∪- or ∩-shape and for determination of initial states according to covariates. Our modeling approach is specific to each transition, so as to obtain a more coherent model. Parallel to competing risks models, the multistate model takes into account several final events. We consider an example of kidney transplant recipient follow-up to illustrate the utility of the method. Copyright © 2007 John Wiley & Sons, Ltd.