In an analysis of capture-recapture data, the identification of a model that fits is a critical step. For the multisite (also called multistate) models used to analyze data gathered at several sites, no reliable test for assessing fit is currently available. We propose a test for the JMV model, a simple generalization of the Arnason-Schwarz (AS) model, in the form of interpretable contingency tables. For the AS model, we suggest complementing the test for the JMV model with a likelihood ratio test of AS vs. JMV. The examination of an example leads us to propose further a partitioning that emphasizes the role of the memory model of Brownie et al. (1993 Biometrics 49, 1173-1187) as a biologically more plausible alternative to the AS model.