Abstract: By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in FC-spaces. By using these equilibrium existence theorems, some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are established in noncompact product FC-spaces. These results improve and
generalize some recent results in literature to product FC-spaces without any convexity structure.

Key words: Maximal element, generalized game, equilibrium, system of generalized vector quasi-equilibrium problems, FC-spaces