This paper is devoted to theoretical aspects in nonlinear optimization, in particular, duality relations for some mathematical programming problems. In this paper, we introduce a new generalized class of second-order multiobjective symmetric G-Wolfe-type model over arbitrary cones and establish duality results under Gf-bonvexity/Gf-pseudobonvexity assumptions. We construct nontrivial numerical examples which are Gf-bonvex/Gf-pseudobonvex but neither η-bonvex/η-pseudobonvex nor η-invex/η-pseudoinvex. © 2020, The Author(s).