A fluid dispenser device including a body and a cover that pivots between a closed position and an open position and reservoirs each containing a dose of fluid. The reservoirs are arranged on a strip and an opening mechanism is provided. The device includes a movable support to move a reservoir against the opening mechanism. The movable support is movable between a non-dispensing position and a dispensing position. The device includes a strip-rolling system having a drum and an actuator member. The actuator member turning relative to the body in a first direction when the movable support is moved from the non-dispensing position towards the dispensing position, and in a second direction when the movable support is moved from their dispensing position towards the non-dispensing position. The actuator member causes the drum to turn only when turning in the second turning direction.
