Dipolar relaxation of multiple quantum (MQ) NMR coherences is investigated theoretically on the evolution period of the MQNMR experiment in chains with an arbitrary number of spins. The dependencies of the intensities of these coherences on the lengths of the evolution and preparation periods are obtained. It is shown that the intensity of the MQ NMR coherence of the zeroth order does not decay completely in the relaxation process. The experimental results obtained for a quasi-one-dimensional chain of 19F nuclear spins in calcium fluorapatite qualitatively agree with the results of the developed theory. (C) 2017 Elsevier B.V. All rights reserved.