This paper extends the class of generalized type Ⅰ functions introduced by Aghezzaf and Hachimi(2000) to the context of higher-order case and formulate a number of higher-order duals to a non-differentiable multi-objective programming problem and establishes higher-order duality results under the higher-order generalized type Ⅰ functions introduced in the present paper.A special case that appears repeatedly in the literature is that the support function is the square root of a positive semi-definite quadratic form.This and other special cases can be readily generated from these results.