In a ferromagnetic or antiferromagnetic crystal the hyperfine coupling between the electrons and the nuclei of the magnetic or nonmagnetic ions leads to a certain broadening of the nuclear resonance line. (This phenomenon is already known for samples in the paramagnetic state.) Via the hyperfine coupling a particular nucleus excites a virtual spin wave, which is reabsorbed by one of the other nuclei. This sequence of events is equivalent to a long range interaction between the nuclear spins. Since the direction of magnetization furnishes a preferred axis, this coupling is anisotropic with respect to this axis. Thus one obtains a reduction in the transverse relaxation time, T2. If there are several nuclear species in the sample under examination, the time T1 may be shortened by the same mechanism, which enables energy to flow from the species under consideration to the other species