An injection device for injection of set doses of medicine from a cartridge has a nut that is screwed up along a threaded piston rod during a dose setting operation. The nut is screwed along the piston rod by rotating a dose setting member. A rotational coupling mechanism includes an axially displaceable coupling member which is rotated as a function of axial displacement. During dose setting, the nut is allowed to rotate relative to the coupling member. During injection, the coupling member is rotationally locked to the nut. This provides a dose setting and injection mechanism wherein the nut member is both rotated during dose setting and during injection.