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A new mixed type nondifferentiable higher-order symmetric dual programs over cones is formulated. As of now, in the literature, either Wolfe-type or Mond&#8722;Weir-type nondifferentiable symmetric duals have been studied. However, we present a unified dual model and discuss weak, strong, and converse duality theorems for such programs under higher-order <inline-formula> <math display="inline"> <semantics> <mi mathvariant="script">F</mi> </semantics> </math> </inline-formula>- convexity/higher-order <inline-formula> <math display="inline"> <semantics> <mi mathvariant="script">F</mi> </semantics> </math> </inline-formula>- pseudoconvexity. Self-duality is also discussed. Our dual programs and results generalize some dual formulations and results appeared in the literature. Two non-trivial examples are given to show the uniqueness of higher-order <inline-formula> <math display="inline"> <semantics> <mi mathvariant="script">F</mi> </semantics> </math> </inline-formula>- convex/higher-order <inline-formula> <math display="inline"> <semantics> <mi mathvariant="script">F</mi> </semantics> </math> </inline-formula>- pseudoconvex functions and existence of higher-order symmetric dual programs.