New theoretical and methodological bases for synthesis of analog and digital control algorithms for actuating systems are presented. Algorithms are built on the basis of the principle of control over accelerations, which gives the designed systems natural properties of adaptability, weak sensitivity to changes in parameters and the action of disturbing forces. The structure of the algorithms is formed directly by the initial nonlinear equations of controlled motion, and the parameters are calculated based on the concepts of inverse dynamics problems from the condition of the implementation of the assigned dynamic characteristics. Applied tasks of synthesis of algorithms of positioning and trajectory control of manipulators, as well as algorithms of control of power operations in assembly robots are considered. The method of synthesis of algorithms of motion control of complex mechanisms by separative models is described.