Waste device for refuse, in particular for diapers and the like, comprising a container having a bottom and a circumferential wall, wherein the container has a container opening on the end remote from the bottom, wherein the waste device is provided with closing means that are positioned near to the container opening for substantially closing the container opening in such a way that odor release is prevented, wherein the closing means comprise: - a drum housing (58,60) provided in the internal part of the waste device, said drum housing (58,60) having a drum opening facing the interior of the container; - a drum body (76,78) having an external surface that is at least partially closely connected to an inner surface of the drum housing (58,60), wherein the drum body (76,78) has a transport container (181, 182) for the refuse, said transport container (181, 182) extending inwardly from the external surface thereof, wherein the drum body (76,78) is pivotable between: an insertion position wherein refuse is placeable in the transport container (181, 182), and a transit position wherein the transport container (181, 182) is aligned with the drum opening; - a flexible sealing member extending about a circumferential edge of the drum opening of the drum housing, wherein the sealing member, as seen in an axial cross-section, comprises a connection part (94, 110) that is located radially outwards, and that is connected to the drum housing, and wherein the sealing member comprises a sealing part (98, 100) connected to the connection part (94, 110), which sealing part (98, 104,100) extends radially inward from the connection part (94, 110) and which may be brought into sealingly contact with the external surface of the drum body (76,78) for sealing the container opening in a substantially odor-free manner, wherein the waste device further comprises a cover configured and arranged to be received on the container, wherein the cover comprises a cover opening for supplying waste to the container, wherein the drum housing (58,60), when the cover is placed on the container, at least partially encloses the drum body (76,78) and wherein, in the insertion position, the transport container (181, 182) is aligned with the cover opening, characterized in that a radial inner end of the sealing part (98, 100) that is remote from the connection part (94, 110) is free from any connection to the drum housing (58,60) such that a freely movable free radial inner end of the sealing member is formed. - a drum housing (58,60) provided in the internal part of the waste device, said drum housing (58,60) having a drum opening facing the interior of the container; - a drum body (76,78) having an external surface that is at least partially closely connected to an inner surface of the drum housing (58,60), wherein the drum body (76,78) has a transport container (181, 182) for the refuse, said transport container (181, 182) extending inwardly from the external surface thereof, wherein the drum body (76,78) is pivotable between: an insertion position wherein refuse is placeable in the transport container (181, 182), and a transit position wherein the transport container (181, 182) is aligned with the drum opening; an insertion position wherein refuse is placeable in the transport container (181, 182), and a transit position wherein the transport container (181, 182) is aligned with the drum opening; - a flexible sealing member extending about a circumferential edge of the drum opening of the drum housing, wherein the sealing member, as seen in an axial cross-section, comprises a connection part (94, 110) that is located radially outwards, and that is connected to the drum housing, and wherein the sealing member comprises a sealing part (98, 100) connected to the connection part (94, 110), which sealing part (98, 104,100) extends radially inward from the connection part (94, 110) and which may be brought into sealingly contact with the external surface of the drum body (76,78) for sealing the container opening in a substantially odor-free manner, wherein the waste device further comprises a cover configured and arranged to be received on the container, wherein the cover comprises a cover opening for supplying waste to the container, wherein the drum housing (58,60), when the cover is placed on the container, at least partially encloses the drum body (76,78) and wherein, in the insertion position, the transport container (181, 182) is aligned with the cover opening, characterized in that a radial inner end of the sealing part (98, 100) that is remote from the connection part (94, 110) is free from any connection to the drum housing (58,60) such that a freely movable free radial inner end of the sealing member is formed. wherein the waste device further comprises a cover configured and arranged to be received on the container, wherein the cover comprises a cover opening for supplying waste to the container, wherein the drum housing (58,60), when the cover is placed on the container, at least partially encloses the drum body (76,78) and wherein, in the insertion position, the transport container (181, 182) is aligned with the cover opening, characterized in that a radial inner end of the sealing part (98, 100) that is remote from the connection part (94, 110) is free from any connection to the drum housing (58,60) such that a freely movable free radial inner end of the sealing member is formed.