Binary fluid ‘Lennard-Jones-mixtures’ of type (μ = σ22/σ11, μ12= σ12/σav12, ν = ϵ22/ϵ11, ν12= ϵ12/ϵav12) with σav12and ϵav12being the arithmetic mean of the corresponding parameters for the like interaction have been studied by molecular dynamics simulations. Similar to a recent work, the static and dynamic cross correlation were determined as a function of the cross parameter ν12. However, in the present investigation the ‘volume parameters’ for the two kinds of particles were different. For this type of mixtures (μ > 1) the border line between stable and unstable systems was found to be at much lower ν12-values than for systems composed of particles of like size (μ = 1·0). The magnitude of the cross correlation agrees however for both types of mixtures. By means of the present systems fluid-fluid phase separation could also be simulated. The system (1·3, 1·05, 2·0, 0·575) shows an inhomogeneous region aroundT* = 3·0 and at pressures of 1500 bar and becomes homogeneous forT* > 4·0.