Thermocapillary flow, driven by a thermally induced surface tension variation along a liquid free surface, is considered. A comprehensive theoretical and experimental research program on the subject carried on at Case Western Reserve University is briefly described. From those studies it became apparent that thermocapillary flows are very complex and that there are several serious limitations to the ground-based work. Therefore, experiments at low-gravity are needed in order to understand better such complex flows. The justification for low-gravity experiments is presented. A description of the space experiments proposed and of the supporting ground work is given. Experiments on thermocapillary flow in reduced gravity are designed to study the following aspects: the extent and nature of thermocapillary flows at large Marangoni number Ma(> 104); temperature distributions along the free surface and in the bulk fluid, and their effect on the flow fields; the effect of heating mode and of the liquid free surface shape on the flows; the onset conditions and nature of oscillatory flows.