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) that can be actuated so as to cause 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, the leading end (25) of said flexible strip (20), in the advance direction of said strip, being fastened to a receiver element (500) that is rotatably mounted, said receiver element (500) being adapted to exert a traction force on said elongate strip (20), said device including an abutment element (5000) that is disposed between said first displacement means (30) and said receiver means (500), said abutment element (5000) co-operating with said flexible strip (20) so as to eliminate said traction force, at least in part, on the portion of the flexible strip that is disposed upstream of said abutment element (5000) in the displacement direction of said flexible strip (20).