A reduced modeling technique for solving electromagnetic diffusion problems is the spectral Lanczos decomposition method (SLDM). In this paper an alternative approach of applying this method to transient electromagnetic diffusion problems is presented. The approach is based on Maxwell's equations as a system of first-order partial differential equations as opposed to the standard SLDM that is based on a second-order partial differential equation for either the electric or the magnetic field strength. By taking the system of first-order equations as a starting point, it is possible to simultaneously construct approximations to the electric and magnetic field strength. Moreover, these approximations are highly structured. The structure of the approximations reflects the structure that is present in the original set of equations. Certain extensions of the present method are also given, and some numerical results for two-dimensional configurations are presented. ¿ 1998 American Geophysical Union