An ostomy appliance 100 is described having a top 101 and bottom 102 and including first and second walls 104, 105 connected to each other at or near their peripheries, the first wall having a stoma-receiving opening106; a waste collecting cavity 103a; and a gas vent 110 provided in either of the first or second walls to permit waste gases to escape from the waste collecting cavity, wherein the gas vent is covered by a cover member 112 which includes an outlet 114 from which communicates with the gas vent, said outlet opening in a direction towards a bottom of the appliance. Also described is an ostomy appliance system including such an ostomy appliance and a blocking member for closing the outlet of the cover member.