In this paper, we formulate Wolfe and Mond–Weir type second-order multiobjective symmetric dual problems over arbitrary cones. Weak, strong and converse duality theorems are established under η -bonvexity/ η -pseudobonvexity assumptions. This work also removes several omissions in definitions, models and proofs for Wolfe type problems studied in Mishra [9]. Moreover, self-duality theorems for these pairs are obtained assuming the function involved to be skew symmetric.