The purpose of this paper is to study invariant submanifolds of an n -dimensional manifold M endowed with an F -structure satisfying F K + ( − ) K + 1 F = 0 and F W + ( − ) W + 1 F ≠ 0 for 1 < W < K , where K is a fixed positive integer greater than 2 . The case when K is odd ( ≥ 3 ) has been considered in this paper. We show that an invariant submanifold M ˜ , embedded in an F -structure manifold M in such a way that the complementary distribution D m is never tangential to the invariant submanifold ψ ( M ˜ ) , is an almost complex manifold with the induced F ˜ -structure. Some theorems regarding the integrability conditions of induced F ˜ -structure are proved.