An interactive boundary-layer method, together with the e"approach to the calculation of transition, is used to predict the stall and post-stall behavior of airfoils in incompressible and compressible flows at low freestream Mach numbers. Two separate inviscid methods—a panel method with compressibility corrections and a full potential method—are used to compute the external velocity distribution needed in the solution of the compressible boundary-layer equations. The turbulence model is based on the Cebeci-Smith algebraic eddy-viscosity formulation with improvements for strong pressure gradient effects. Comparison of calculated results with inviscid flow computed with a panel method indicate excellent agreement with experiment for a wide range of Reynolds numbers in incompressible flows. Comparison of calculated results obtained with inviscid flow computed with a full potential method also indicate excellent agreement with experiment for a wide range of angles of attack, including stall for compressible flows at low freestream Mach numbers. The study also shows that even though the compressibility corrections to the panel method are adequate at small-to-moderate angles of attack, they are not satisfactory at higher angles of attack, especially near stall.