In this paper we study nonoccurrence of the Lavrentiev phenomenon for a large class of nonconvex optimal control problems identified with the corresponding complete metric space of integrands M, which satisfy a growth condition common in the literature and are Lipschitzian on bounded sets. We establish that for most elements of M ( in the sense of Baire category) the in. mum on the full admissible class of trajectory-control pairs is equal to the in. mum on a subclass of trajectory-control pairs whose controls are bounded by a certain constant.