Experimental and theoretical investigations of dynamics and relaxation of multiple quantum (MQ) nuclear magnetic resonance (NMR) coherences of the zeroth and second orders are performed in a quasi-one-dimensional chain of nuclear spins of 19F in calcium fluorapatite. MQ NMR dynamics are studied on the preparation period of the MQ NMR experiment in the approximation of nearest neighbor interactions. The density matrix of the system at the end of the preparation period is used as the initial condition for the study of the relaxation process on the evolution period of the MQ NMR experiment. The relaxation asymptotics of the intensity of the MQ NMR coherence of the zeroth order is obtained. Relaxation of the MQ NMR coherence of the second order is investigated with ZZ part of the dipole-dipole interactions. The experimental data qualitatively agree with the results of the developed theory