Summary: By employing the notion of exceptional family of elements, we establish some existence results for weakly efficient solutions for mixed vector variational inequality problems. We show that the nonexistence of an exceptional family of elements is a necessary condition for the solvability of mixed vector variational inequality problems. By using the asymptotic mappings of vector-valued mappings, we present a sufficient condition for the nonexistence of an exceptional family of elements for mixed vector variational inequality problems in reflexive Banach spaces, and obtain some existence results for weakly efficient solutions for mixed vector variational inequality problems. When the operator is affine and copositive, we present a sufficient condition for the nonexistence of an exceptional family of elements for mixed affine vector variational inequality problems, establish some existence results for weakly efficient solutions of mixed affine vector variational inequality problems, and provide some sufficient conditions for solution sets of mixed affine vector variational inequality problems to be nonempty and compact. The existence results of solutions for scalar mixed variational inequality problems in finite dimensional spaces are generalized to mixed vector variational inequality problems in reflexive Banach spaces.