Two distinctly different reduced-order models are formulated for fully nonlinear aeroelastic systems. The first is based on Proper Orthogonal Decomposition (POD). The velocity field is decomposed into a finite number of orthonormal modes, effecting order reduction by transforming from physical space to a low-dimensional eigenspace. The second model is based on the method of Harmonic Balancing (HB). It retains the same physical dimensions of a high-order CFD model but transforms from the time domain to the frequency domain, requiring a single solution for each harmonic frequency included in the model. The number of harmonic frequencies is much smaller than the number of time steps required in a time-accurate simulation. Comparisons are made between POD and HB model output and experimental data for a set of canonical problems involving viscous effects, now separation, and fully nonlinear aeroelastic behavior: now past a stationary cylinder, a cylinder with forced oscillations, and a self-excited, plunging cylinder. Copyright © 2005 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.