This paper combines a nonlinear frequency-domain scheme with a high-order spectral-difference discretization for the two-dimensional unsteady Euler equations. An implicit lower/upper symmetric Gauss-Seidel method is introduced to solve the nonlinear frequency-domain equations. High-order accuracy and solution acceleration due to the implicit treatment are numerically verified on the vortex advection and subsonic airfoil test cases. Finally, the performance of this implicit high-order scheme on a fully compact stencil for periodic flows is evaluated on a pitching-airfoil problem.