An assembly consisting of a container (1) having a nozzle (17) for dispensing a substance contained in the container (1), and a cap (19) for covering the nozzle (17), the container having a first connection region (14) which can be connected to a corresponding second connection region (25) of the cap (19), the connection regions (14, 25) being selected such that the container (1) and the cap (19) are connected at least partially by a rotational movement of the container (1) and the cap (19) relative to one another, the cap (19) having an inner chamber (20) surrounded by a casing (22), which chamber is open at one end so as to receive the nozzle (17), the casing (22) having an end face (21) at its open end, and the container (1) having a cover face (12) which points toward the cap and has a cover edge (11), the connection regions (14, 25) being selected and the end face (21) being adapted to the cover face (12) and the cover edge (11) thereof such that, when the container (1) and the cap (19) are connected, the end face (21) comes into contact with the cover face (12) when the cap (19) is in a first intermediate position and, when the container (1) and the cap (19) are rotated further relative to one another, the end face (21) is pressed against the cover face (12) and the cap (19) ultimately reaches a second end position, the end face (21) passing over the cover edge (11).