Implicit appproximate-factorization (AF) algorithms are developed for the solution of steady-state transonic flow problems. The performance of the AF solution method is evaluated relative to that of the standard solution method for transonic flow problems, successive line over-relaxation (SLOR). Both methods are applied to the solution of the nonlinear, two-dimensional transonic small-disturbance equation for flows about representative transonic airfoils. Results indicate that the AF method requires substantially less computer time than SLOR to solve the nonlinear finite-difference matrix equation for the flowfield. This increase in computational efficiency is achieved with virtually no increase in computer storage or coding complexity.