Abstract: Let E.F be topological vector spaces over the field Φ(which is either the real field R or the complex field C).let<,>:=F×E→Φ be a bilinear functional.and let X be a nonempty subset of E.Given a multi-valued map S:X→2^x,two multi-valued maps M.T:X→2^F and a function h:X×X→ R, the generalized bi-quasi-variational inequality problem (GBQVIP)is to find a point ŷ ∈ X such that ŷ∈S(ŷ) and inf_w∈T(ŷ).Re(f-w,ŷ-x) + h(ŷ,x) ≤ 0 for all x ∈ S(ŷ) and for all f ∈M(ŷ).In this paper,we obtain three general existence theorems on solutions of GBQVIPs which simultaneously unify,sharpen and extend the corresponding results of Shih-Tan and Zhou-Chen to paracompact setting.