Device for fastening a tarpaulin on a frame or a container or, preferably, on a lorry body or the like, comprising a frame profile to be fastened to the frame and a tarpaulin profile which interacts with said frame profile and is releasably connectable thereto and has a connection for a tarpaulin holder or a piping holder, a) it being possible for the tarpaulin profile to be introduced into the frame profile by a turn-and-slide movement, b) at least a part or a region of at least one of the two profiles (2, 7) being elastically deformed, optionally in the contact region, c) there being, in the mounted state, a form-fitting contact in at least one non-elastically deformed region of the contact between the frame profile and the tarpaulin profile, characterised in that d) either the frame profile has a curved slot (14, 22) into which a curved tongue (16, 20) of the tarpaulin profile can be inserted in a rotating manner, in that an outer lip of the frame profile bears resiliently against the tongue (16, 20), and in that the form-fitting contact is provided approximately opposite the lip in the region of an inner corner of the tarpaulin profile and an outer corner of the frame profile; or in that the frame profile has a holding groove extending obliquely to the frame surface, preferably in a curved manner, and a guide groove extending differently obliquely, preferably in a curved manner, in that the tarpaulin profile has a holding strip and a guide strip which can be introduced into the grooves assigned to said strips (23, 22) under elastic deformation of the region of the tarpaulin profile between said strips by means of a turn-and-slide movement, and in that the form-fitting contact is provided on the holding groove facing the tarpaulin, on the groove wall facing the tarpaulin. a) it being possible for the tarpaulin profile to be introduced into the frame profile by a turn-and-slide movement, b) at least a part or a region of at least one of the two profiles (2, 7) being elastically deformed, optionally in the contact region, c) there being, in the mounted state, a form-fitting contact in at least one non-elastically deformed region of the contact between the frame profile and the tarpaulin profile, characterised in that d) either the frame profile has a curved slot (14, 22) into which a curved tongue (16, 20) of the tarpaulin profile can be inserted in a rotating manner, in that an outer lip of the frame profile bears resiliently against the tongue (16, 20), and in that the form-fitting contact is provided approximately opposite the lip in the region of an inner corner of the tarpaulin profile and an outer corner of the frame profile; or in that the frame profile has a holding groove extending obliquely to the frame surface, preferably in a curved manner, and a guide groove extending differently obliquely, preferably in a curved manner, in that the tarpaulin profile has a holding strip and a guide strip which can be introduced into the grooves assigned to said strips (23, 22) under elastic deformation of the region of the tarpaulin profile between said strips by means of a turn-and-slide movement, and in that the form-fitting contact is provided on the holding groove facing the tarpaulin, on the groove wall facing the tarpaulin.