Binary mixtures of two identical Lennard-Jones fluids with non-Lorentz-Berthelot combining rules have been simulated over the entire concentration range at three state points in order to examine the effect of cross interactions on the mixing properties, excess volumes and enthalpies, and partial molar volumes. and on the structure. Various combinations of deviations, in both the energy and size cross parameters, from the Lorentz-Berthelot rule, have been considered and the results analyzed using a recently proposed method based on the Tikhonov regularization. It is found that the most important is the size cross parameter and that by varying the combining rules a variety of qualitatively different behavior can be produced including, e.g., a minimum in the partial molar volumes observed otherwise only in complex mixtures of associating fluids; occurrence of this minimum seems to be associated with changes in the second coordination shell as witnessed by the pair correlation function. (c) 2008 Elsevier B.V. All rights reserved.