A thermodynamics approach to the description of the dynamic boundary angle is proposed. An energy equation for the moving line of contact of three media is derived taking into account viscous Row, The energy equation is used to substantiate the boundary condition of the asymptotic theory for the free boundary slope angle at a small distance from the solid. Second-order asymptotic relations of the dynamic wetting theory are developed assuming a low capillary constant. Boundary conditions for Navier-Stokes equations over a moving three-phase contact line for a general how of viscous liquid are derived. A solution procedure for the case of low Reynolds numbers is considered. Assuming a stationary movement of the interface in a capillary, a method for establishing the second-order terms is proposed. Exact asymptotic solutions are obtained. Symmetry of theasymptotic relation for the dynamic boundary angle in the principal approximation is described.