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In this paper, we study the relationships between the Stampacchia and Minty vector variational inequalities and vector continuous-time programming problems under generalized invexity and monotonicity hypotheses. We extend the results given by other authors for the scalar case to vectorial one, and we show the equivalence of efficient and weak efficient solutions for the multiobjective continuous-time programming problem, and solutions of Stampacchia and Minty variational-like type inequality problems. Furthermore, we introduce a new concept of generalized invexity for continuous-time programming problems, namely, the Karush–Kuhn–Tucker (KKT)-pseudoinvexity-II. We prove that this new concept is a necessary and sufficient condition for a vector KKT solution to be an efficient solution for a multiobjective continuous-time programming problem. In this work, duality results for Mond–Weir type dual …