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We introduce and study a class of η-generalized vector variational-like inequalities and a class of η-generalized strong vector variational-like inequalities in the setting of Hausdorff topological vector spaces. An equivalence result concerned with two classes of η-generalized vector variational-like inequalities is proved under suitable conditions. By using FKKM theorem, some new existence results of solutions for the η-generalized vector variational-like inequalities and η-generalized strong vector variational-like inequalities are obtained under some suitable conditions.