Closure system for a leakproof baby feeding bottle comprising - a lower closure ring which has a substantially cylindrical lower peripheral part with an internal thread, which may be screwed onto an external thread of a bottle and comprises a lower partition connected to the lower peripheral part on the edge above the internal thread and blocking its cross section, with a first upper face and a first lower face and at least one lower throughflow hole which opens, on the one hand, in the first upper face and, on the other hand, in the first lower face, - an upper closure ring which comprises a substantially cylindrical upper peripheral part with an external thread for connecting to a screw ring for fastening a drinking teat to the upper peripheral part and an upper partition connected to the upper peripheral part on the upper edge and blocking its cross section, with a second upper face and a second lower face located sealingly on the first upper face and at least one upper throughflow hole which opens, on the one hand, in the second lower face and, on the other hand, in the second upper face, - locking elements which rotatably and releasably lock together the lower closure ring and the upper closure ring relative to one another, - a circular lip seal made of a soft elastic material concentric to the 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 the upper peripheral part being arranged on the 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 the lower throughflow hole.