In the operation of a syringe pump, the plunger (54) of a syringe (50) is continuously driven by a motor (30), the translational propulsion of the plunger being superimposed with a rotational movement. To this end, a movable screw (20) is connected either directly or via an adaptor to the plunger (54) of the syringe (50), the syringe being clamped by means of a clamping device (40) in front of the housing (10) of the novel syringe pump. The screwing movement of the movable screw (20) through the screw nut (22) is transferred to the plunger (54). The movable screw (20) is connected to the shaft (36) of the continuously working motor (30) directly, by way of a transmission (60) or reduction gear (60). The device allows the highly precise and continuous delivery of the syringe content while avoiding slip-stick effects.