Using a state of the art computational fluid dynamic (CFD) method to model nonlinear steady and unsteady transonic flows in conjunction with a linear structural model, an investigation is made into how nonlinear aerodynamics can effect the divergence, flutter, and limit cycle oscillation (LCO) characteristics of a transonic airfoil configuration. A single degree of freedom (DOF) model is studied for divergence, and one and two DOF models are studied for flutter and LCO. A harmonic balance method in conjunction with the CFD solver is used to determine the aerodynamics for finite amplitude unsteady excitations of a prescribed frequency. A procedure for determining the LCO solution is also presented. For the configuration investigated, nonlinear aerodynamic effects are found to produce a favorable transonic divergence trend, and unstable and stable LCO solutions respectively for the one and two DOF flutter models.