An expression for the shear viscosity of molecular liquids is derived from the statistical expression for the stress tensor by taking into consideration density fluctuations over the intermolecular force range. The viscosity formula consists of a low density term given in terms of the Chapman-Enskog viscosity and a density dependent term reminiscent of the Stokes-Einstein relation between the viscosity and the self-diffusion coefficient. According to this formula, the shear viscosity of molecular liquids can be calculated in terms of intermolecular site-site forces, the corresponding pair correlation functions, and the self-diffusion coefficient as well as the Chapman-Enskog viscosity at low density. By treating the viscosity expression as a semiempirical formula where the experimental and numerically simulated self-diffusion coefficients available in the literature are used, the shear viscosities of nitrogen and carbon dioxide, both of which are treated as a rigid linear rotator with two sites, are calculated and compared with experiment. Agreement between theory and experiment is found very good qualitatively and quantitatively. (C) 2000 American Institute of Physics. [S0021-9606(00)51616-X].