Abstract In this paper, a new class of generalized invex functions named generalized uniform pseudoinvex (C, q) – type I, generalized uniform pseudoquasi-invex (C, q) – type I and generalized uniform quasipseudo-invex (C, q) – type I are defined by utilizing the Clarke subdifferential, where C is sublinear in the third argument. Then some sufficient optimality conditions are derived and proved for a class of nondifferentiable multiobjective programming problems involving the new generalized uniform invexity.