A drug to be infused into a patient is contained in a syringe or vial having a displaceable plunger for ejecting the drug out through an injection port into an administration set. Motion of the plunger of the drug delivery syringe/vial is controlled by a driver syringe having a piston or plunger for ejecting either a compressible or an incompressible fluid through a flow resistance element. Motive power for the piston of the drive syringe is provided by a constant load spring. A suitable linkage is provided for coupling the piston of the drive syringe to the plunger of the drug delivery syringe. Several types of flow rate control elements for use with the driver syringe are disclosed.