A fluid dispenser device a body in which the direction in which an actuating element (5) moves is different from, and in particular perpendicular to, the axial direction in which the piston or the valve member of the dispensing member moves, the actuating element (5) having an end portion provided with the cam surface (6) which co-operates with the reservoir (3) or a fixing ring (8) adapted to fix the dispensing member to the reservoir (3) so that the actuating element (5) being moved substantially radially into its actuating position causes the reservoir (3) to be moved axially relative to the piston or to the valve member of the dispensing member so as to dispense a dose of fluid.