AbstractA system of equations is derived for the evolution under action of cross‐relaxation (CR) of the dipole–dipole reservoir (DDR) and Zeeman subsystems, redefined taking into account the fact, that the part of secular dipole‐dipole interactionH′d, which causes homogeneous displacement of spin resonant frequencies at low temperatures (LT) must be subtracted fromH′d. The case is considered, when the influence of the change of LT displacement due to CR on the energy, absorbed by DDR, is stronger, than that of the usual high‐temperature term. It is shown, that in this situation both, DDR and spins under CR acquire a negative temperature in spite of the fact, that the frequency of saturated spins is smaller than the frequency of spins under CR. This behaviour differs from the high‐tempe