In this paper we consider the generalized vector equilibrium problem $(P_{\alpha})$ of 0nding a point $z_0, x_0)\in E \times K$ such that $x_0 \in A(z_0, x_0)$ and $$\forall \eta\in A(z_0,x_0), \exists z\in B(z_0,x_0,\eta), \quad (F(z,x_0,\eta), C(z,x_0,\eta))\in \alpha,$$ where $\alpha$ is an arbitrary relation on $2^Y$, and $A,B,C$ and $F$ are set-valued maps between finite-dimensional spaces. Existence results are obtained under assumptions di3erent from those of [17]. Some special cases of Problem $(P_{\alpha})$ are discussed in detail.