A fluid dispenser device comprising a body (10), said device further including: an elongate flexible strip (20) supporting a plurality of reservoirs (21) each containing a dose of fluid or powder; reservoir-opening means (30) for opening a respective reservoir on each actuation; first displacement means (40) 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 (45) for displacing a full reservoir (21) against said opening means (30) each time the device is actuated, the leading end (25) of said flexible strip (20), in the advance direction of said strip, being fastened to a receiver element (50) that is rotatably mounted relative to said body (10), said receiver element (50) being adapted to exert a traction force on said elongate strip (20), said traction force being independent of said first displacement means (40), said traction force being applied on said strip when said second displacement means (45) move the empty reservoir (21) away from said opening means (30) after each actuation.