The thermocapillary movement of bubbles has been investigated for large Reynolds numbers. A numerical analysis of the flow field around a bubble has been carried out for arbitrary Marangoni (Ma) numbers. For small Ma the flow field has been calculated using a matched asymptotic procedure. A comparison is made of the nondimensional bubble velocity and the temperature gradient at the bubble surface, calculated numerically, with analytical results for large and small values of Ma, and with numerical results obtained previously. The expansion for large Ma has also been proposed by Balasubramaniam and Subramanian (1996). For Ma much greater than 1 the presence of both the thermal boundary layer and the wake impose limitations in the numerical calculations. The calculations have been carried out for values of Ma significantly larger than those previously obtained.