Résumé : We consider the problem of variable selection in general nonlinear mixed-e ets models, including mixed-e ects hidden Markov models. These models are used extensively in the study of repeated measurements and longitudinal analysis. We propose a Bayesian Information Criterion (BIC) that is appropriate for nonstandard situations where both the number of subjects N and the number of measurements per subject n tend to in nity. In this case, the consistency rates of the maximum likelihood estimators (MLE) of the parameters depend on the level of variability designed in the model. We show that the MLE of the population parameters related to subject-speci c parameters are \sqrt(N)-consistent whereas the MLE of the parameters related to xed parameters are \sqrt(Nn)-consistent. We derive a BIC criterion with a penalty based on two terms proportional to log(N) and log(Nn). Finite-sample properties of the proposed selection procedure are investigated by simulation studies.