Summary Although multistate mark–recapture models are recognized as important, they lack a simple model-selection procedure. This article proposes and evaluates a step-up approach to select appropriate models for multistate mark–recapture data using score tests. Only models supported by the data require fitting, so that over-complicated model structures with too many parameters do not need to be considered. Typically only a small number of models are fitted, and the procedure is also able to identify parameter-redundant and near-redundant models. The good performance of the technique is demonstrated using simulation, and the approach is illustrated on a three-region Canada goose data set. In this case, it identifies a new model that is much simpler than the best model previously considered for this application.