Airbag for a vehicle occupant restraint system and airbag module

The airbag has a wall which in the unfolded state of the airbag defines a recess (30) with a mouth (28) or opening over which locates a cover component (40) fastened to the airbag wall. The cover component is formed from at least two overlapping sections which each have an edge section not fastened to the airbag wall. The two non-attached edge sections are arranged with an offset in relation to each other. The cover sections are fabric elements (42,44) sewn to the wall of the airbag.