This paper demonstrates the use of nonlinear normal modes to predict limit cycle oscillation in a pitch-plunge airfoil with cubically nonlinear pitch stiffness. Aeroelastic systems with quasi-steady and unsteady aerodynamics are analyzed with nonlinear normal modes. An alternative derivation of nonlinear normal modes using first-order form is offered for systems that cannot fit the standard second-order form. The effect of the master coordinate chosen to construct the nonlinear normal modes is examined and found to have a significant impact on the accuracy of the results. Based on the results herein the nonlinear normal mode method is found to be a viable approach to studying and predicting limit cycle oscillation in aeroelastic systems. Furthermore, a master coordinate based on the the linear flutter mode was found to lead to the best results.