Two-layer flows with evaporation at interface are studied. Exact solutions of a stationary problem are constructed. At fixed boundaries the no-slip conditions, temperature, a condition for vapor concentration on the upper fixed boundary are given. Following conditions are fulfilled at thermocapillary non-deformable interface: kinematic and dynamic conditions, continuity of velocity and temperature, condition for heat transfer at interface, mass balance relation and a relation for saturated vapor concentration. Examples of velocity profiles are presented.

Key words: convection in a fluid, thermocapillary interface, evaporation through the interface, interface conditions, exact solutions.