Given a group G, we show how one can define a vague group structure on G via a chain of subgroups of G. We discuss how a group homomorphism f from a vague group X onto a group Y induces a vague group structure on Y with f satisfying the vague homomorphism property. The notion of Ω-vague groups is introduced, where Ω is a fuzzy subset. The direct product G1 × G2 of two vague groups and the internal vague direct product of subgroups of a vague group is introduced.