This work aims to estimate the limitations of the van der Waals one-fluid (vdW1) approximation in the prediction of the viscosity of Lennard-Jones (LJ) mixtures. To do so, non-equilibrium molecular dynamics simulations have been performed. Results on mixtures have been compared to those of their equivalent pure fluids (in the sense of the vdW1 model). Several systems (146 configurations) are studied, which are composed of binary and ternary mixtures in various thermodynamic states and for different combining rules. In a first step, deviations induced separately by LJ molecular parameters (size or energy) have been analyzed. It is shown that the vdW1 model is well designed for the energy parameter in every configuration. On the contrary, for the size parameter, deviations induced by this one-fluid approach are shown to be large in dense state and low temperature systems. In a second step, the coupling effects of the LJ size and energy parameters with the mass are studied. It appears that an accurate one-fluid approximation for viscosity should involve a coupling between the mass and the size parameters in its formulation (which is not the case with the vdW1 model) but not between the mass and the energy. (c) 2006 Elsevier B.V. All rights reserved.