In this paper, we consider nonlinear nonconvex optimal control problems and study convergence conditions of their solutions. To be more precise, we first introduce a generalized boundedness condition and discuss its relations with some typical existing ones in the literature. Next, combining this condition with the Gronwall Lemma, we investigate the boundedness property of solutions to state equations and the compactness of feasible sets of the reference problems. Then, based on these obtained results, convergence conditions in the sense of Painlevé-Kuratowski for such problems are formulated. Finally, at the end of the paper, applications to two practical situations, problems of fuel-optimal frictionless horizontal motion of a mass point and glucose models, are also presented.