In numerical simulations of microwave structures using the alternating-direction implicit finite-difference time-domain (ADI-FDTD) method, the time marching scheme comprises two sub-iterations, where different updating schemes for evaluating E and H fields at each sub-iteration can be adopted. In this paper, the E-field implicit-updating (EFIU) and H-field implicit-updating (HFIU) schemes are compared with each other especially with regard to the implementation of local boundary conditions.