The effect of magnetic fields in different direction, on the instability of thermocapillary convection in a rectangular cavity, with differentially heated side walls, filled with two viscous fluids, is investigated in the absence of gravity. The computational results show that, the electromagnetic damping of the hydrothermal wave instability under z-direction magnetic field is the most efficient, that of y-direction magnetic field is the second, and the magnetic field parallel to the x-direction results in the weakest damping. Furthermore, for imposing on any magnetic fields in arbitrary orientation, the hydrothermal wave instability can be fully suppressed when the magnetic field intensity is enough large. (C) 2010 Elsevier Ltd. All rights reserved.