Mathematical modeling of the convective processes caused by impact of various forces on the fluid and gas media is rather important nowadays. The increased interest to these problems is caused also by the preparation of experiments on the International Space Station in the frame of the scientific project "Convection and Interfacial Mass Exchange" (CIMEX) of the European Space Agency. They are the experiments to investigate the convective flows of the fluids with a thermocapillary interface between liquid and gas phases. In the case, when a gas flow generates the tangential stresses on a free boundary of liquid, the additional characteristics of the convective flows should be identified. In this paper a stationary coupled problem of gravitational, thermocapillary convection in a horizontal layer with free boundary under conditions of a co-current gas flow is studied. The kinematic and dynamic conditions are fulfilled exactly on the gas-liquid interface. The exact solutions for different types of thermal boundary conditions have been obtained. An evaporation effect through the gas-liquid interface is modeled qualitatively with the help of a heat transfer condition. It has been found that the direction of the velocity at the gas-liquid interface is determined by the governing parameters. The equal-zero condition for the interface velocity has been found, as well. The paper presents the velocity and temperature profiles in the conditions, which correspond qualitatively to the CIMEX experiments. (C) 2010 Elsevier Ltd. All rights reserved.