The Tonelli existence theorem in the calculus of variations and its subsequent modiΓΏcations were established for integrands f which satisfy convexity and growth conditions. In Zaslavski (Nonlinear Analysis 43 (200l) 339), a generic well-posedness result (with respect to variations of the integrand of the integral functional) without the convexity condition was established for a class of optimal control problems satisfying the Cesari growth condition. In Zaslavski (Communications in Applied Analysis, to appear) we extended this generic well-posedness result to a class of variational problems in which the values at the end points are also subject to variations. More precisely, we established a generic well-posedness result for a class of variational problems (without convexity assumptions) over functions with values in a Banach space E which is identiΓΏed with the corresponding complete metric space of pairs (f; ( 1; 2)) (where f is an integrand satisfying the Cesari growth condition and 1; 2 β E are the values at the end points) denoted by A. We showed that for a generic (f; ( 1; 2)) β A the corresponding variational problem is well posed. In this paper we study the set of all pairs (f; ( 1; 2)) β A for which the corresponding variational problem is well posed. We show that the complement of this set is not only of the ΓΏrst category but also a -porous set.