Generalized algebraic operations introduced by Ben-Tal [5] are used to define new classes of generalized convex functions, namely (h, φ)-(b, F, ρ)-convex functions and generalized (h, φ)-(b, F, ρ)-convex functions in the vectorial case. Further, optimality and duality results are proved for the considered h, φ-nondifferentiable multiobjective programming problem under assumptions that the functions involved are (generalized) (h, φ)-(b,F, ρ)-convex.