The closure device (500) comprises a stopper (501) made of elastomer and a cover (502) suitable for covering both the neck (12) of a container and stopper (501) in place in said neck (12). The cover (502) is made of plastics material and comprises a ring (503) and a drive member (504). The ring (503) may surround the stopper (501) and the neck (12) in the mounted configuration, the ring being provided with locking means (503G) for locking on the neck (12). The drive member (504) may be mounted on the ring (503) in arbitrary angular orientation about a central axis (X503) of the ring. The drive member is provided with an annular edge (505D) suitable for being engaged between an outer skirt (503A) of the ring (503) and at least one tab (503G) forming locking means and extending radially towards the central axis (X503) of the ring from the skirt (503A).