An implicit adaptive Nonlinear Frequency Domain method (NLFD) has been developed and validated for the Navier-Stokes equations on deformable grids. Although the computational time for periodic flows is reduced by using the NLFD approach in comparison with classical time marching schemes, the adaptive NLFD approach leads to additional reductions in the overall computational effort. A novel adaptation strategy that allows both mode augmentation and reduction enables the adaptive approach to gain a factor of two reduction in memory and computational cost at anequivalent solution accuracy to the non-adaptive approach. In order to further accelerate the convergence, the non-linear LU-SGS technique, which is an implicit time marching approach, is implemented. In the non-linear LU-SGS method, the computational cells are treated locally; hence, its implementation is quite suitable for the adaptive NLFD method, where different cells have dierent number of modes and therefore has to be treated individually. Through an innovative approach, each mode is updated separately within each cell, while the coupling eects of the other modes,which are included in the Fourier expression of the solution are transferred to the right-hand side and are iteratively updated. As a result, the computational efficiency of the implicit solver is not decreased as the number of modes increases. Through the developed implicit solver, more than one order of magnitude speed up is obtainedcompared to the modied ve-stage Runge-Kutta explicit approach. Finally, the concept of dynamic or moving/deformable grid is extended to the present approach for numerical simulation of physical periodic problems, where the flow periodicity is induced from a moving/deforming object. The approach is validated for 2D laminar vortex shedding behind stationary, plunging, and pitching cylinder and airfoil cases.