The vibrational energy relaxation (VER) rates for H-2 and D-2 in liquid argon (T = 152 K, rho = 1.45 x 10(22) cm(-3)) are calculated using the linearized semiclassical (LSC) method (J. Phys. Chem. 2003, 107, 9059, 9070). The calculation is based on Fermi's golden rule. The VER rate constant is expressed in terms of the quantum-mechanical force-force correlation function, which is then estimated using the LSC method. A local harmonic approximation (LHA) is employed in order to compute the multidimensional Wigner integrals underlying the LSC approximation. The H-2-Ar and D-2-Ar interactions are described by the three-body potential of Bissonette et al. (J. Phys. Chem. A1996, 105, 2639). The LHA-LSC-based VER rate constants for both D-2 and H-2 are found to be about 2-3 orders of magnitude slower than those obtained experimentally. However, their ratio agrees quantitatively with the corresponding experimental result. In contrast, the classical VER rate constants are found to be 8-9 orders of magnitude slower than those obtained experimentally, and their ratio is found to be qualitatively different from the corresponding experimental result.