Summary: In this paper, we consider nonlinear multiobjective optimal control problems and investigate the convergence conditions of their feasible solution sets and efficient solution sets. Firstly, we utilize the Lipschitz continuity of the function on the right-hand side of the state equation and the uniform continuity of the objective map to analyze the convergence of the sequence of feasible solution sets in the sense of Painlevé-Kuratowski and the continuous convergence of the sequence of objective maps. Subsequently, we employ these obtained results in conjunction with the properties of the generalized convexity integrand of the objective map to formulate the upper and lower Painlevé-Kuratowski convergence of efficient solution sets. Furthermore, when the data of the reference problems do not satisfy the generalized convexity conditions, we employ the induction condition along with a key hypothesis to address the upper and lower Painlevé-Kuratowski convergence of the efficient solution sets. Finally, as applications of the obtained results, we discuss convergence conditions for two practical scenarios involving the glucose and epidemic models.