The defect-diffusion model is based on the proposed existence of one mechanism for relaxation which is that, at any molecular site, relaxation can only occur when a defect diffuses to the site. The dynamic, non-equilibrium distribution of individual diffusing defects is considered, so that the treatment relates to non-equilibrium processes occurring at a microscopic level. Unlike many other physical models of relaxation it does not consider averaged defect concentrations, and averaged arrival-rates of defects. When an analysis by Glarum of the defect-diffusion model is applied to viscoelastic relaxation an infinite viscosity is predicted. This result arises from the invalidity at long times of one of the physical assumptions he adopted. A corrected analysis is found to be mathematically intractable and hence a series of mathematical approximations have been developed with a physically acceptable long-time response together with the original satisfactory short-time response of Glarum's treatment. The first approximation is trivial; however, the second approximation (when Laplace-transformed) is identical to the model proposed by Barlow, Erginsav and Lamb to describe their viscoelasticity results for a large number of supercooled non-polymeric molecular liquids. It is demonstrated that the defect-diffusion model might be expected to apply to this class of liquids but not to certain other classes and that a defect could be a hole of molecular dimensions.