Results for quantum-mechanical calculations of the integral cross sections and corresponding thermal rate coefficients for para-/ortho-H-2 + HD collisions are presented. Because of significant astrophysical interest in regard to the cooling of primodial gas the low temperature limit of para-/ortho-H-2 + HD is investigated. Shape resonances in the rotational state-resolved cross sections have been calculated at low energies. These resonances are important and significantly contribute to the corresponding rotational state-resolved thermal rate coefficients, particularly at low temperatures T less than or similar to 100 K. Additionally, the cross sections for elastic HD + HD have been calculated. As compared to the two other calculations for H-2 + HD we obtained mixed results, confirming one case but differing in the second case. In our treatment of HD + HD we obtained satisfactory agreement with both theoretical and experimental expectations. (C) 2009 Elsevier B. V. All rights reserved.