The 'network solution' technique for obtaining numerical solutions to Maxwell's equations in two-dimensional inhomogeneous media, originally developed by Madden, is presented in detail in this paper. By using plane-wave and infinite line-current sources respectively, theoretical magnetotelluric and Turam responses can be calculated above and within an arbitrarily complex two-dimensional earth conductivity structure. Analysis of a few representative model results emphasizes the importance of considering all the electromagnetic field components, particularly those of the anomalous field. In magnetotellurics, the vertical magnetic field is useful in determining strike direction, and only the E parallel apparent resistivities are representative of deep structure in the presence of near-surface conductivity inhomogeneities. In Turam, a finite resistivity background causes buried conductors to appear deeper and more conductive than they would appear if the background had infinite resistivity; and strong conductors can affect the total field sufficiently to cause screening.