Abstract: The paper introduces the concepts of strongly superefficient solution, C-strongly superefficient solution, weakly superefficient solution, C-weakly superefficient solution, homogeneously superefficient solution and C-homogeneously superefficient solution for vector equilibrium problems, and discusses the dual forms of  C-weakly superefficient solution, C-superefficient solution, C-homogeneously superefficient solution, C-strongly superefficient solution, respectively for vector equilibrium problems in locally convex space with the aid of polar theory. The equivalence of the above kinds of superefficiencies in the normed space was studied, and their dual forms for vector equilibrium problems in the normed space with a normal cone were discussed. As an application, the dual forms of various superefficiencies are given for vector optimization problems.

Key words: vector equilibrium problems, vector optimization, strongly superefficient solution, weakly superefficient solution, homogeneously superefficient solution, dual form