The paper deals with various aspects of reducing mechanical oscillations arising in multi-axis electromechanical systems containing flexible members, pendulum mechanisms, etc. It is based on many years of experience, not only in the theoretical field, but especially in numerous experiments on physical systems operating on various principles, including robotic arms, cranes, mobile robotic chassis, and various other manipulation mechanisms. The possibility of applying damping feedback is mentioned. Since this approach may have several implementation limitations, the principles of oscillations reduction based on shaping control signals in one or more degrees of freedom are also introduced. Problems with underactuated structures and the emergence of resonant oscillations are also discussed.