AIAA Paper No. 98-0517, 36th AIAA Aerospace Sciences Meeting, Reno, Nevada, Jan. 1998.An unsteady, two-dimensional, incompressible potential-flow solver and an unsteady, two-dimensional, compressible Euler/Navier-Stokes flow solver are coupled with a two-degree-of-freedom structural model for the time-domain computation of aeroelastic response. Comparisons are made between results from the two flow solvers and with flutter boundary predictions of linear theory. Presented results demonstrate similar destabilizing effects for both increasing airfoil thickness and increasing Mach number. More importantly, it is shown that linear theory yields un-conservative flutter-velocity predictions. While linear theory predicts that single-degree-of-freedom (pitching) flutter cannot occur except with an unrealistically high sectional moment of inertia, it is shown here that thicker airfoils in compressible flows may easily achieve single-degree-of-freedom flutter under realistic conditions