A fluid dispenser device comprising a body (10) provided with a dispenser orifice (15), said device further comprising: an elongate flexible strip (20) supporting a plurality of reservoirs (21) each containing a dose of fluid reservoir-opening means (80) for opening a respective reservoir on each actuation first displacement means (30) for causing said flexible strip (20) to advance before and/or during and/or after each actuation, so as to bring a full reservoir into register with said reservoir-opening means and second displacement means (50) for displacing a full reservoir (21) against said opening means (80) each time the device is actuated, said device including positioning means (300) that are adapted to position the full reservoir accurately relative to the reservoir-opening means (80) when it is displaced thereagainst, so as to guarantee that opening is predetermined and reproducible on each actuation.