The EPR linewidth dependence on temperature and impurities concentration in KMn1-xMexF3 single crystals (where Me is Ni2+, Co2+, Fe2+) is investigated both experimentally and theoretically. The theoretical investigation is performed with the use of a nonequilibrium statistical operator method proposed by Zubarev (1971). The microscopic kinetic equations of motion for the magnetisation of the host and impurities subsystems are derived and the width of the resonance line is calculated. The theoretical results and compared with the experimental data.