The influence of the Marangoni effect on the stationary motion of a drop with uniform internal heat generation immersed in a homogeneous fluid is considered. The hydrodynamical force acting on the drop is calculated. We show that the force can be either drag or thrust. We also identify thresholds for instability. In particular, a weakly nonlinear analysis around the monotonic instability threshold for drop translations is carried out. It is shown that in the absence of buoyancy and depending on parameter values, besides the motionless state, a regime of autonomous, i.e., self-sustained, drop motion can appear, either supercritically or subcritically. In the subcritical case with vanishing Biot number, the finite amplitude excitation of the autonomous motion is analyzed. We show that the dependence of the hydrodynamical force on the drop velocity is nonmonotonous thus bringing the possibility of multiple steady states. For instance, for some values of the force and a given level of buoyancy, up to five different flow velocities are found with, however, only two of them being actually stable. Various other possibilities that appear when the Marangoni number is varied are also discussed. (C) 1994 Academic Press, Inc.