We have studied the thermocapillary motion of a drop in a fluid under
nonequilibrium conditions, in the presence of velocity and temperature
gradients, After reformulating the boundary value problem in terms of
an induced force and an induced heat source densities, we have derive
d the Faxen theorem for the drop. The theorem gives the hydrodynamic f
orce exerted on the drop as a function of its velocity and of the unpe
rturbed velocity and temperature fields. From it we infer expressions
for the mobility and thermocapillary coefficients. Our general result
then permits us to analyze a number of particular situations of intere
st which have been reported by other authors.