The generation of reduced-order models for computing the unsteady and nonlinear aerodynamic loads on an aircraft from pitching motions in the transonic speed range is described. The models considered are based on Duhamel’s superposition integral using indicial (step) response functions, Volterra theory using nonlinear kernels, radial basis functions, and a surrogate-based recurrence framework, both using time-history simulations of a training maneuver(s). Results are reported for the X-31 configuration with a sharp leading-edge cranked delta wing geometry, including canard/wing vortex interactions. The validity of the various models studied was assessed by comparison of the model outputs with time-accurate computational-fluid-dynamics simulations of new maneuvers. Overall, the reduced-order models were found to produce accurate results, although a nonlinear model based on indicial functions yielded the best accuracy among all models. This model, along with a time-dependent surrogate approach, helped to pr...