  We study the decay of multiple quantum (MQ) NMR coherences in systems with
the large number of equivalent spins. As being created on the preparation
period of MQ NMR experiment, they decay due to the dipole-dipole interactions
(DDI) on the evolution period of this experiment. It is shown that the
relaxation time decreases with the increase in MQ coherence order {(according
to the known results)} and in the number of spins. We also consider the
modified preparation period of MQ NMR experiment (G.A.Alvarez, D.Suter, PRL
{\bf 104}, 230403 (2010)) concatenating the short evolution periods under the
secular DDI Hamiltonian (the perturbation) with the evolution period under the
non-secular averaged two-spin/two-quantum Hamiltonian. The influence of the
perturbation on the decoherence rate is investigated for the systems consisting
of 200-600 equivalent spins.
