This paper describes the application of the theoretically based scheme of Vesovic and Wakeham, modified by making use of the hard-sphere model of Dymond and Assael, to the prediction of the viscosity of liquid mixtures. The purpose of the paper is to examine this scheme in more detail than earlier to find out in what circumstances it works well and when it fails. Hence, the scheme is employed to predict, for the first time, the viscosity of a wide range of mixtures of quite disparate liquids from groups of hydrocarbons, through combinations of alcohols and hydrocarbons, to halogenated refrigerants. It is shown that, in all cases, provided that the mass ratio of the pure components is close to unity, the predictions show excellent agreement with experiment.