[en] The partially averaged version of classical S-matrix theory was applied to three-dimensional collisions of H₂ with He and Li⁺. For H₂--Li⁺, cross sections for the de-excitation of H₂ from (n₁,j₁) = (1,0) to the ground vibrational manifold were computed at a total energy of 1.2 eV and compared to previously done coupled-channel calculations of Schaefer and Lester. The agreement is very good. For H₂--He, the Kutzelnigg--Tsapline interaction potential was extended to small atom--diatom separations, the ab initio points were then fit to an analytic form, and cross sections for the de-excitation of H₂ from the states (n₁,j₁), n₁ = 1, j₁ = 0,2,4 to the ground vibrational manifold were computed at total energies of .9, 1.1, 1.3 and 1.5 eV. For comparison, coupled-channel calculations were also performed on the system at the same energies. The agreement was poorer than in the H₂--Li⁺ case, for identifiable reasons. The cross sections were used to compute rate constants and relaxation times for the H₂--He system. Comparison of these results with the results of experiment and of other calculations shows good agreement, certainly within the expected errors