The effects of transverse curvature, shock-generated external vorticity, boundary-layer displacement, and wall slip and temperature jump are considered as first-order boundary-layer effects. The classical boundary-layer equations were modified to include the higher-order effects, and flows over a 9-deg half-angle blunt cone were considered at M∞ = 9 and 18. Comparisons are made with second-order theory and experimental data. Primary interest is given to predicting the higher-order effects on zero-lift drag and comparsion with experimental data. Range of applicability of higher-order boundary-layer theory is indicated based upon the ability to predict zero-lift drag. Vorticity was the dominant higher-order effect, and the theory is most applicable to relatively short slender bodies. At very low Reynolds numbers, strong coupling of the higher-order effects was found to exist.