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<p/> <p>We introduce and study a class of <inline-formula> <graphic file="1029-242X-2010-968271-i2.gif"/></inline-formula>-generalized vector variational-like inequalities and a class of <inline-formula> <graphic file="1029-242X-2010-968271-i3.gif"/></inline-formula>-generalized strong vector variational-like inequalities in the setting of Hausdorff topological vector spaces. An equivalence result concerned with two classes of <inline-formula> <graphic file="1029-242X-2010-968271-i4.gif"/></inline-formula>-generalized vector variational-like inequalities is proved under suitable conditions. By using FKKM theorem, some new existence results of solutions for the <inline-formula> <graphic file="1029-242X-2010-968271-i5.gif"/></inline-formula>-generalized vector variational-like inequalities and <inline-formula> <graphic file="1029-242X-2010-968271-i6.gif"/></inline-formula>-generalized strong vector variational-like inequalities are obtained under some suitable conditions.</p>