Effects of scalar spin-spin interactions on the nuclear magnetic relaxation dispersion (NMRD) of coupled multispin systems were analyzed. Taking spin systems of increasing complexity we demonstrated pronounced influence of the intramolecular spin-spin couplings on the NMRD of protons. First, at low magnetic fields where there is strong coupling of spins the apparent relaxation times of the coupled spins become equal. Second, there are new features, which appear at the positions of the nuclear spin level anticrossings. Finally, in coupled spin systems there can be a coherent contribution to the relaxation kinetics present at low magnetic fields. All these peculiarities caused by spin-spin interactions are superimposed on the features in NMRD, which are conditioned by changes of the motional regime. Neglecting the effects of couplings may lead to misinterpretation of the NMRD curves and significant errors in determining the correlation times of molecular motion. Experimental results presented are in good agreement with theoretical calculations.