A combined experimental and theoretical study of the NMR spin-lattice relaxation times for the deuteron of D-2 in D-2-Ar mixtures is presented. A gas-handling system and a sample cell have been designed and successfully employed in the experimental part of this study. Spin-lattice relaxation times for the deuteron of D-2 in D-2-Ar mixtures have been measured over the temperature range 180-420 K at several densities and mole fractions, and extrapolation to infinite dilution has been carried out. The quality of the results has been tested by analysis of the one-dimensional spectra. Theoretical values of the spin-lattice relaxation times associated with the D-2-Ar interaction have been calculated using the XC(fit) potential energy surface obtained by Bissonnette ct al. [J. Chem. Phys. 105, 2639 (1996)]. Two reliable methods have been proposed to compare the theoretical and experimental NMR spin-lattice relaxation times obtained for the equilibrium mixture of the two parity isomers of the D-2-Ar system under conditions in which separate measurement of their deuteron relaxation times is not possible. The agreement between experimental and theoretical results is found to be relatively good only for higher temperatures. These results indicate that the anisotropies of the XC(fit) potential energy surface need refinement.