This　paper　addresses　multiwindow　Gabor　systems　on　discrete　periodic　sets,　which　can　model　signals　to　appear　periodically　but　intermittently.　We　give　some　necessary　and/or　sufficient　conditions　for　multiwindow　Gabor　systems　to　foe　frames　on　discrete　periodic　sets,　and　characterize　two　multiwindow　Gabor　Bessel　sequences　to　foe　dual　frames　on　discrete　periodic　sets.　For　a　given　multiwindow　Gabor　frame,　we　derive　all　its　Gabor　duals,　among　which　we　obtain　an　explicit　expression　of　the　canonical　Gabor　dual.　In　addition,　we　generalize　multiwindow　Gabor　systems　to　the　case　of　a　different　sampling　rate　for　each　window,　and　investigate　multiwindow　Gabor　frames　and　dual　frames　in　this　case.　We　also　show　the　properties　of　the　multiwindow　Gabor　systems　are　essentially　not　changed　by　replacing　the　exponential　kernel　with　other　kernels.