In the paper a class of families (M) of functions defined on differentiable manifolds M with the following properties: $1_{}$. if M is a linear manifold, then (M) contains convex functions, $2_{}$. (·) is invariant under diffeomorphisms, $3_{}$. each f ∈ (M) is differentiable on a dense $G_{\delta }$-set, is investigated.