In the present paper the application of a laminar boundary-layer theory, previously developed by the authors, to the problem of the maximum-lift coefficient of airfoils is discussed. The calculations are carried through in detail for a first approximation, called a single-roof profile, to the potential velocity distribution over the upper surface of an airfoil. The results indicate a large variation in Clmax with turbulence but the quantitative dependence on Reynolds’ number and turbulence is not satisfactory. The calculations are then repeated for a so-called double-roof profile which approximates to the flow over the upper surface of an N.A.C.A. 2412 airfoil. These results are compared with those obtained from an experimental investigation on the same airfoil. The agreement is considered to indicate that for moderate values of R and Clmax the phenomenon of the maximum-lift coefficient is controlled by a contest between the separation and transition points of the laminar boundary layer over the nose of the airfoil. The difficulties involved in extending the theory to larger values of R, or to airfoils whose Cl vs. α curves are not approximately linear up to the stall, are mentioned.