A hydrodynamical description of supernova remnants is based on the approximation of locally equilibrium particle distributions. Shock waves in supernova remnants at various stages of ejecta propagation are collisionless and form nonequilibrium particle distributions that relax slowly to quasiequilibrium distributions within a time longer than the hydrodynamic time. A kinetic model of the heating of ions behind the front of a shock wave in the SN 1987A remnant is considered with allowance for a complex chemical composition of the ejecta, and nonequilibrium distributions of ions in the vicinity of this shock wave are calculated. In addition to the quasi-Maxwellian peak, which determines the effective temperature of a given charge state of an ion, nonequilibriumdistributions of ions contain, in some cases, a suprethermal component, which may describe to the injection of ions in the process of cosmic-ray acceleration.