The paper considers nonlinear waves generated on a surface of a horizontal liquid layer put into an assigned stress field at the gas-liquid interface. The nature of branching for wavy modes from the undisturbed flow was studied. To accomplish this, the solution of a model nonlinear equation written for the deviation of the layer thickness from the undisturbed layer is found. Analytical solutions were constructed for nonlinear steady state-travelling solutions of this equation with the wavenumbers belonging to the vicinity of neutral wavenumbers. Steady state-travelling periodic solutions for the first family were simulated for the case of wavenumbers beyond this vicinity.