Summary: Two-dimensional equations of steady motion for second order fluids are expressed in a special coordinate system generated by the potential flow corresponding to an inviscid fluid. For the flow around an arbitrary object \(\phi\) coordinates are the streamlines, \(\psi\) coordinates are the velocity potential lines. It is clear that the equations of motion so derived and boundary conditions become in a sense independent of the body shape immersed into the flow. Using the usual boundary layer assumptions the boundary layer equations are then deduced from the equations of motion by employing a technique of matched asymptotic expansion.