The foundations of a new scientific direction in the mechanics of bodies of variable mass, associated with the concept of non-stationary reactivity and currently called hyperreactive mechanics, are presented. Using the differential principle of completeness, equations of hyperreactive motion were found, the main feature of which is the presence of quantities that depend on the acceleration of the change in the mass of the system. The main attention is paid to the analysis of the properties of the phenomena under consideration, their accurate mathematical description.