The locomotion of a viscous drop induced by an internal secretion of a weak surface-active substance is considered. The system consists of a viscous drop that contains another smaller droplet at an off-center location and is embedded in an unbounded viscous fluid that is free of the surfactant far from the drop. The inner droplet has a uniform concentration of the secreted material, while a non-adsorbing kinetics is used for the mass flux across the surface of the larger drop. The mass transfer results in a non-uniform distribution of interfacial tension at the outer surface and induces a Marangoni flow there and a migration of the fluid particles. The dependence of the velocities of the drops migration on the distance between the centers and on governing parameters such as the ratios of the viscosity and diffusivity of the phases is studied for the cases when the motion is induced solely by the Marangoni effect and under the combined action of gravity and thermocapillarity. Non-linear effects of convective transport at low and high Peclet numbers and of surface deformations are presented. (C) 2004 Elsevier Ltd. All rights reserved.