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 $$\mathrm{\forall }\eta \in A(z_0,x_0),\mathrm{\exists }z\in B(z_0,x_0,\eta ),(F(z,x_0,\eta ),C(z,x_0,\eta ))\in \alpha ,$$ 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.