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The model is an extension of the mixed effects linear model including an unspecified function of time<jats:italic>f<\/jats:italic>(<jats:italic>t<\/jats:italic>). The estimator<jats:italic>f\u0302<\/jats:italic>(<jats:italic>t<\/jats:italic>) is defined as the solution of the maximization of the penalized likelihood and is approximated on a basis of cubic M\u2010spline with a reduced number of knots. We present modifications of four criteria (cross\u2010validation, generalized cross\u2010validation, T of Rice, Akaike's criterion) to estimate the smoothing parameter when data are correlated; these four criteria gave very similar results in the simulation study. The simulation study showed also the superiority of the Bayesian confidence bands of the mean curve over the frequentist ones. We develop empirical Bayes estimates of subject\u2010specific deviations. This approach was applied to study the progression of CD4+ lymphocyte counts in a cohort of HIV patients treated with protease inhibitors. 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