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A new fully-implicit approach for computing tran-sonic aeroelastic solutions is presented. The nn-steady Euler equations are coupled with a typical section swept wing model and integrated forward in time. The implicit Euler equations are integrated in pseudo-time using multigrid methods, and are coupled with a first-order system decomposition of the structural modal equations. Full convergence of the simultaneous governing equations is achieved at every time step with considerable computational savings over previous approaches. Transient responses for a NACA 64, 4010 are calculated in different flow regimes, and flutter boundaries are computed and compared to pre-existing numerical data.