The work deals with the problem of hydrodynamic stability in liquid systems containing surfactants. The detailed analysis was focused on a thin liquid film with an adsorbed monolayer. In this system, the interface undergoes a tangential stress due to the surface tension gradient promoted by a moving barrier. A simplified mathematical model of the system hydrodynamics showed that the flow instability (cell convection) could be observed for certain values of parameters characterized by the critical value of the Reynolds number. This instability also leads to the change of mass transfer mechanism. Some experimental evidence of this effect was found From the Langmuir balance studies. The described phenomenon can be responsible for efficient mass transfer in some technological and biological surfactant-liquid systems.