A closure system for a baby bottle including a lower closure ring screwed onto an external thread of a bottle, an upper closure ring for connecting to a screw ring for fastening a drinking teat, locking elements which rotatably and releasably lock together the lower closure ring and the upper closure ring, a circular lip seal made of a soft elastic material concentric to a lower peripheral part being arranged on the first upper face, with at least one axially oriented sealing lip and at least one circular seal geometry engaging with the lip seal and concentric to an upper peripheral part being arranged on a second lower face or vice versa and by rotating the upper closure ring relative to the lower closure ring the upper throughflow hole may optionally be brought into overlapping and non-overlapping positions relative to a lower throughflow hole.