A theoretical study of multicomponent mass transfer in liquid-liquid extraction systems at microscale is carried out using the standard extraction system water/toluene/acetone/MIPK. We focus on the diffusional interactions between the transferred components, the so-called cross effects, and investigate the conditions at which these effects can significantly influence multicomponent mass transfer behaviour at microscale. For this purpose, a rigorous mathematical model is developed based on the Stefan-Maxwell equations. Another, less rigorous model that does not consider cross effects is built up using effective diffusion coefficients. The latter model is used as a reference, because such models are widely used for the description of multicomponent mass transfer in conventional macroscopic devices. Both models are implemented into a commercial CFD software. The comparison of the simulation results obtained by both approaches permits the impact of cross-effects to be estimated. Microchannel dimensions and the contact time of the two immiscible phases, which flow countercurrently, are varied over a large range. Furthermore, different mass transfer directions are examined. It is found that the cross effects can considerably influence mass transfer behaviour and hence extraction performance at small-scale microchannel dimensions and sufficiently large contact times. The intensity of this influence largely depends on the component transfer direction.