A combined experimental and theoretical study of the nuclear magnetic resonance (NMR) spin-lattice relaxation times for the proton and deuteron of HD in HD-Ar mixtures is presented. Spin-lattice relaxation times for the proton and deuteron of HD in HD-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. Theoretical values of the spin-lattice relaxation times associated with the HD-Ar interaction have been calculated using the XC(fit) potential energy surface obtained by Bissonnette et al. [J. Chem. Phys. 105, 2639 (1996)], transformed to allow displacement of the center-of-mass of the HD molecule from its center-of-force. Both experimental and theoretical results show that the density-dependence of the deuteron relaxation times lies in the linear regime, while that of the proton lies in the non-linear regime. The experimental and theoretical results for the relaxation times of the proton are in excellent agreement. The corresponding results for the deuteron are in good agreement (within a few percent); the agreement is, however, not as good as it is for the proton. These results indicate that the transformed XC(fit) potential energy surface represents the anisotropic part of the HD-Ar interaction rather accurately. It is argued that the improved quality of the XC( fit) potential energy surface for the heteronuclear HD-Ar interaction is due to the large contribution that the isotropic part of the homonuclear potential surface makes to the anisotropic part of the heteronuclear potential surface.