The large area-to-volume ratio of microreactors gives prospect of better yield and selectivity than for conventional designs, since diffusive fluxes of mass and heat in micro-devices scale with area, while the rate of changes corresponding to sources and sinks are proportional to volume. Indeed, theoretical considerations of the scaling behaviour (see [1]) support the fact that micro-reactors allow for faster chemical reactions and provide better thermal control. Moreover, specific applications prove that these advantages of micro-reactors can be realised in order to perform fast exothermic reactions (cf. [2-4]) and to enhance selectivity [5]. For such applications, the mixing of chemical species is of special interest, since it is an essential condition for chemical reactions. To obtain efficient mixing for the short residence times in micro-systems, the contact area between regions of higher and lower species concentration has to be increased significantly. To avoid large pressure drops, secondary flows instead of turbulent flow fields are preferred. In case of a T-shaped micro-mixer, the secondary flow acts mainly in cross directions, i.e. perpendicular to the axial direction, and can be used to mix the two feed streams. To assess and optimise the mixing process, this qualitative picture has to be understood more thoroughly and significant quantitative information has to be added. In particular, the interplay of convective and diffusive transport to bridge the gap between the reactor and the molecular scale, have to be further investigated, since even if no new physico-chemical phenomena occur, new aspects enter the picture in case of micro-systems; cf. [6] and the references given there. The present paper employs CFD-simulations to obtain first steps in this direction.