Although differential screw mechanisms are widely used in precision mechanisms to control fine relative movements, their enumeration and systematic methods of analysis seem less widespread. In this paper methods to support the preliminary design steps of these devices are proposed. In particular, has been proposed an enumeration algorithm of screw mechanisms. This method makes use of kinematic structure relationships deduced by Kraus (1951, Getriebelehre, Verlag Technik, Berlin; 1952, Gründlagen des Systematischen Getriebeaufbaus, Verlag Technik, Berlin). Kinematic and static analyses of differential screw mechanisms are described mainly in the German technical literature. However, such analyses are based on graphical constructions. In the paper graph-based analytical methods of kinematic, static and mechanical efficiency analyses are proposed. Examples of application of the suggested methods are offered.