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We prove some existence results of solutions for a new class of generalized bi-quasivariational inequalities (GBQVI) for quasi-pseudomonotone type II and strongly quasi-pseudomonotone type II operators defined on noncompact sets in locally convex Hausdorff topological vector spaces. To obtain these results on GBQVI for quasi-pseudomonotone type II and strongly quasi-pseudomonotone type II operators, we use Chowdhury and Tan's generalized version (1996) of Ky Fan's minimax inequality (1972) as the main tool.