This paper present a multidomain pseudospectral method for accurately solving Maxwell's equations in the time domain. The scheme is developed for computing scattering by two-dimensional smooth perfectly conducting objects like circular or elliptic cylinders in free space and utilizes a Fourier collocation method in the azimuthal direction and a multidomain Chebyshev collocation method in the radial direction. Proper absorbing boundary conditions are discussed and a new perfectly matched layer (PML) method in polar coordinates is constructed and shown to be superior to other PML methods. For the elliptic cylinders we propose to use a matched layer in connection with the multidomain approach and a cubic grid mapping. Numerical results of monochromatic electromagnetic scattering by circular and elliptic perfectly electrically conducting cylinders are presented. Comparisons between results obtained using the multidomain pseudospectral method and the finite-difference time domain method clearly illustrate the superiority of spectral methods in obtaining accurate values for the scattered fields and the bistatic radar cross section. (C) 1997 Academic Press.