1) Device for the cleaning of an applicator of liquid or pasty cosmetic products consisting of a substantially cylindrical body (1), crossed by an axial hole (4), to be applied to the neck of a container and which shows a terminal section (3) having a substantially truncated conical layout, characterized in that the outer wall (7) of this terminal section which reaches the applicator, forms, with the device axis, an angle different from 90° and in that the device wall, at least in this terminal section, tapers until to have a null thickness in correspondence with the edge (8).