This　paper　addresses　general　super　Gabor　systems　with　rational　time-frequency　product　lattices.　A　Zak　transform　matrix　method　is　developed　for　such　super　Gabor　systems.　We　characterize　complete　super　Gabor　systems　and　super　Gabor　frames.　Given　a　super　Gabor　frame,　we　obtain　an　explicit　expression　of　its　canonical　dual　and　a　parametrization　of　all　its　super　Gabor　duals　and　prove　that　the　canonical　dual　is　the　norm-minimal　one　among　all　super　Gabor　duals.　We　also　prove　that　a　super　Gabor　frame　has　a　unique　super　Gabor　dual　if　and　only　if　it　is　a　Riesz　basis.　(C)　2013　Elsevier　Inc.　All　rights　reserved.