Inthispaper,westudysomenewsystemsofgeneralizedquasi-variationalinclusionproblemsinFC-spaceswithoutconvexitystructure.Byapplyinganexistencetheoremofmaximalelementsofset-valuedmappingsduetotheauthor,somenewexistencetheoremsofsolutionsforthesystemsofgeneralizedquasi-variationalinclusionproblemsareprovedinnoncompactFC-spaces.Asapplications,someexistenceresultsofsolutionsforthesystemofquasi-optimizationproblemsandmathematicalprogramswiththesystemsofgeneralizedquasi-variationalinclusionconstraintsareobtainedinFC-spaces.