Transonic flutter characteristics have been studied for a two degree-of-freedom typical section model with a free-play nonlinearity in both pitch and plunge. The unsteady aerodynamic forces on the airfoil were evaluated using two-dimensional unsteady Euler code and the resulting aeroelastic equations were integrated numerically to obtain time histories of the nonlinear airfoil motion. In this study, limit cycle behaviors and some comparisons for the previous work were presented for the structurally linear and nonlinear models. In addition, the presence of multiple flutter points in the equvalent swept-wing model is also demonstrated. The subsonic, transonic and supersonic flutter boundaries for both structurally linear and nonlinear cases are compared to demonstrate the structural nonlinearrity effect on the flutter stability. The results are presented for several freeplay conditions. From these results, the regions of limit cycle oscillation are observed at the lower velocities than the divergent flutter velocities of the linear structure model. But, in the case of freeplay nonlinearity with the plunge degree of freedom only, the flutter boundary is similar to that of the linear structure model.