The processes of nuclear spin waves (NSW) relaxation in the easy plane type antiferromagnets (AFEP) are investigated. It is shown that in the large NSW spectrum pulling case one must take into account the multiple interactions between the nuclear spins in addition to the Suhl-Nakamura interaction. In the framework of the spin operators diagram technique the NSW relaxation frequencies are calculated in a wide temperature region. In the range

(ω
nis unpulled NMR frequency) the processes of NSW scattering on the longitudinal nuclear spins component fluctuations dominate the NSW relaxation rate in the main part of a momentum space. The influence of the dipole-dipole interaction, paramagnetic impurities and the crystal inhomogeneities on the NSW damping is taken into account. The results obtained are in a reasonable agreement with the experimental data.