This article addresses the analysis of crossover designs with nonignorable dropout. We study nonreplicated crossover designs and replicated designs separately. With a primary objective of comparing the treatment mean effects, we jointly model the longitudinal measures and discrete time to dropout. We propose shared‐parameter models and mixed‐effects selection models. We adapt a linear‐mixed effects model as the conditional model for the longitudinal outcomes. We invoke a discrete‐time hazards model with a complementary log‐log link function for the conditional distribution of time to dropout. We apply maximum likelihood for parameter estimation. We perform simulation studies to investigate the robustness of our proposed approaches under various missing data mechanisms. We then apply the approaches to two examples with a continuous outcome and one example with a binary outcome using existing software. We also implement the controlled multiple imputation methods as a sensitivity analysis of the missing data assumption.