A technique for applying the impedance matrix localization (IML) method in conjunction with the fast multipole method (FMM), termed the hybrid IML-FMM, is presented. This technique significantly reduces the matrix-vector multiplication time in the iterative solution of the method of moment equations arising from the integral-equation-based analysis of two-dimensional electromagnetic scattering phenomena. The reduction in computational time is accomplished through an IML-based sparsification of the FMM far-field transformation matrices. Numerical experiments illustrate the effect of various IML-FMM truncation parameters on the sparsity obtainable, the corresponding reduction in matrix-vector multiplication time, and the solution accuracy. ¿ 1998 American Geophysical Union