Abstract. In this paper we deal with the following generalized vector variational inequality problem: let X, Y and Z be topological vector spaces, K be a convex set in X, D be a nonempty set in Y , and C be a closed convex cone in Z. Let T : K → 2 D be a multifunction andWe prove some existence theorems in which T can be discontinuous, or K can be unbounded, and a existence theorem in which T is pseudomonotone.