A fluid dispenser device including a body (10) with a dispenser orifice (1), a plurality of reservoirs (21) on a strip (20) that includes a leading end (25) and a trailing end (28), a reservoir-opening mechanism (30) adapted to open a respective reservoir upon actuation, and a drive mechanism (40) for the strip (20) and bring a reservoir into register with the opening mechanism. A movable wall (500; 600, 601) separates a storage housing (11) for the elongate strip (20) from a reception housing (15), the elongate strip (20) disposed mainly in the storage housing (11) before the device is used and displaced progressively in the reception housing (15) during use. The movable wall (500) causes the volume of the storage housing (11) to decrease progressively, and the volume of the reception housing (15) to increase progressively.