The review examines the effect of radio-frequency superradiance during pulsed mechanochemical activation of polymer composites under high pressure. Mechanochemical activation is implemented in three modes: (a) rheological explosion of polymer composite under rapid uniaxial compression, when an elastic wave pulse occurs in a polymer composite sample and implements the physico-chemical transformations leading to the occurrence of a superradiance pulse; (b) parametric mode, when an elastic wave pulse is introduced from the outside through a waveguide into a composite sample; (c) the mode of rapid pressure release, which also leads to the occurrence of a superradiance pulse. Paramagnetic polymer composites—namely polystyrene–binuclear clusters Co(QH)2–O–Co(QH)2or Mn(QH)2–O–Mn(QH)2, where QH is a ligand based on QH2–3,6-di-tert-butylpyrocatechin)—are considered as objects implementing such processes. These binuclear clusters exhibit the Dzyaloshinskii–Moriya effect, and polymer composites based on them exhibit multiferroic properties. A composite of a molecular magnet in polystyrene matrix (Eu(III)(SQ)3·bipy complex with four unpaired electrons on Eu(III) and on SQ ligands; SQ is 3,6-di-tert-butylquinolate paramagnetic ligand) is also considered. The binuclear clusters and europium complexes form 2D nano-objects in the polymer matrix with a diameter of 50–100 nm and a thickness of ~ 1–2 nm. The review considers the formalisms of Dicke, Lorentz, Landau–Lifshitz–Blombergen and Havriliak–Negami equations, which make it possible to conduct a time–frequency analysis of these processes, to obtain data on the relaxation processes of spin and charge density in objects responsible for the process of radio-frequency superradiation. It is also shown that the analysis of electron spin resonance data allows us to provide a probable quantum chemical scheme for the implementation of the radio-frequency superradiance process. The phenomenon of superradiation has a great deal of potential in such areas as energy-saving technologies, wireless power transmission and storage devices. The technique of studying fast mechanochemical processes considered in the review allows us to investigate the mechanisms of interaction of magnetic and electrical subsystems in multiferroics and molecular magnets, which expands the scientific base for the creation of new functional materials and enables the solving of related problems of condensed matter physics.