A drive screw having an axial bore is disposed within a tubular container. A cap for closing the container has mounted therefrom an applicator that is insertable in the bore of the drive screw. A first seal and a second seal, on the drive screw, form with the inner wall of the container and the outer wall of the drive screw an annular compartment for housing a cosmetic composition. A normally closed channel is provided between the compartment and the bore of the drive screw. A drive on the cap and a complementary drive on the drive screw cooperate with the first seal and the second seal to decrease the volume of the compartment in which the composition is housed each time the container is opened by removing the cap. A valve opens the channel in response to the decrease in volume in the compartment when the cap is removed so as to permit composition to flow through the channel into the bore of the drive screw to contact the applicator.