Here we apply and extend the material of Part 1 (Mech. Mach. Theory 25, 1-10; 1990), systematically studying all the screw systems in the screw space, corresponding to motions of one, two and three freedoms. We establish a "normal form" for every screw system, namely the most concise representation in terms of base screws. Since, in Part 1, the principle of reciprocity of screws is shown to correspond to a polarity in the screw space, there is no need for a detailed survey of screw systems of a higher order than three. © 1990.