Most routine strategies of motion control in vibration protection systems are based on attenuation of resonant responses using external semi-active or active dampers. In the systems with negative and quasi-zero stiffness, it is simpler because there is no need to know and continually process random signal data from an external vibration source. The control focuses on maintaining a certain balance between the positive and negative stiffness of parametric elements varied in predetermined ranges to keep separation of the system natural frequency spectra and the frequencies of forced vibrations including near-zero values. The control criteria, formulated and quantitatively estimated, provide extremely small stiffness, immobility in a steady state motion, and stabilization in a transient motion of the system without an external damper. The control strategy is validated through designing the systems supplied with active pneumatic suspensions and passive mechanisms of variable negative stiffness. The control algorithms were realized with the help of a two-channel control system and actuators made of commercial hardware and operating in parallel. Efficiency of the algorithms has been estimated through comparison of results of computer simulation and development test of seat suspensions for vibration protection of drivers of heavy trucks and buses and for helicopter pilots.