Presented is a discrete adjoint approach for computing steady and unsteady aerodynamic design sensitivities for compressible viscous flows about airfoil configurations. The nominal flow solver method is based on a harmonic balance solution technique, which is capable of modeling both steady and nonlinear periodic unsteady flows. The computer code for the discrete adjoint solver, which is derived from the nominal harmonic balance solver, has been generated with the aid of the advanced automatic differentiation software tool known as TAF (Transformation of Algorithms in Fortran). © 2003 by Jeffrey P. Thomas, Kenneth C. Hall, and Earl H. Dowell.