In clinical studies, the treatment effect may be heterogeneous among patients. It is of interest to identify subpopulations which benefit most from the treatment, regardless of the treatment's overall performance. In this study, we are interested in subgroup identification in longitudinal studies when nonlinear trajectory patterns are present. Under such a situation, evaluation of the treatment effect entails comparing longitudinal trajectories while subgroup identification requires a further evaluation of differential treatment effects among subgroups induced by moderators. To this end, we propose a tree-structured subgroup identification method, termed "interaction tree for longitudinal trajectories", which combines mixed effects models with regression splines to model the nonlinear progression patterns among repeated measures. Extensive simulation studies are conducted to evaluate its performance and an application to an alcohol addiction pharmacogenetic trial is presented.