In previous work, we found that the normal force responses in poly(methyl methacrylate) (PMMA) and poly(ethyl methacrylate) (PEMA) subjected to torsional deformations were strongly influenced by their prominent P-relaxation mechanisms which are related to the n-alkyl methacrylate side group motions. Using the concept of an elastic stress relaxing material we were able to extract the derivatives of the strain energy density function with respect to the first and second invariants of the deformation tensor (W-1 and W-2). In the present work, we report results from two materials, polysulfone (PSF) and polycarbonate (PC), with weak beta-relaxations that are due to main chain motions. We find that for the two materials, the difference from neo-Hookean behavior is real though very small, contrary to the large deviations from neo-Hookean behavior observed for PMMA and PEMA. The results support the contention that the large normal force responses and the consequent strongly non neo-Hookean behavior of the glassy n-alkyl methacrylates is due to the side chain. (c) 2005 Elsevier Ltd. All rights reserved.