Nonlinear transonic/supersonic flows over an airfoil are studied comparatively using two computational codes, AZTRAN and TMOC, based on the small-disturbance theory. While AZTRAN is unified for all Mach numbers in the transonic regime, TMOC is restricted to the shock-attachment case. Computed results are verified with each other and with those of the ATRAN2 code, the linear theory, and other data whenever appropriate. Cases studied include inverse airfoil design, computation of pressure for an airfoil in pitching oscillations, and calculation of stiffness and damping moments. Finally, calculations of bending-torsi on flutters according to linear and nonlinear theories are presented for a sharp and a blunt-leading-edge airfoil. Our findings indicate that the nonlinearity plays an essential role in this transonic regime.