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In this paper, an alternating-direction implicit (ADI) scheme is applied to the finite-difference time-domain (FDTD) method for solving electromagnetic scattering problems in a generalized coordinate system. A formulation for two dimensional problems is presented and its numerical dispersion and stability property are discussed. In our generalized approach, the nonorthogonal grid is used to model the complex region of a scatterer only, whereas the standard FDTD lattice is used for the remaining regions. As a result, accurate griddings with a simple algorithm can be obtained using the new scheme, and the complexity of the algorithm is minimal. The perfectly matched layer (PML) is used to truncate the boundary. To illustrate the theory, a sinusoidal plane wave and a Gaussian pulse that propagates through a space modeled by locally nonorthogonal grids are used, with the stability of the code examined. The radar cross section of a perfectly conducting cylinder with a thin coating, a large curvature, and/or a sharp edge is calculated using the proposed method, and the result is compared with those using other conventional FDTD methods. It is found that the proposed algorithm is much more efficient than its FDTD counterpart when a complex object is analyzed.