Using an inviscid flow computational-fluid-dynamic model and a harmonic balance flow solver, a parametric investigation of how structural-inertial parameters and freestream Mach number of a transonic flow affect the limit-cycle oscillation characteristics of a typical two-degree-of-freedom transonic airfoil configuration is presented. The computational efficiency of the harmonic balance aerodynamic model allows a much more thorough exploration of the parameter range than has been possible previously.