In 1926, Carson solved the equation for the self and mutual impedances of a conductor in the presence of a semi-infinite homogeneous earth. In his solution for the magnetic field, results were expressed in terms of convergent infinite series. At a later stage, Wise extended the analysis to allow for the effects of displacement currents when the relative permittivities in earth and dielectric are not equal. Recently, Mullineux and Reed showed that Carson's integral solution could be derived by making use of double Fourier transforms, and, at the same time, they generalised the method by permitting the relative permeability to be other than unity. In the paper, the method of double-integral transforms is used to solve the field equation for the self and mutual impedances of a multiconductor system in the presence of a semi-infinite nonhomogeneous earth. The earth is assumed to consist of a homogeneous stratum of a specified depth of one resistivity above a second homogeneous semi-infinite earth of different resistivity. The solution is expressed as an infinite integral, and it is general in the sense that there is no restriction on the permeabilities, permittivities or resistivities of the regions. The effect of displacement currents is taken into account, and the resulting integral is similar in form to that derived by Wise. Numerical results are presented to show the effect of the parameters under a number of specified conditions. Thus, for example, it is indicated that the nonhomogeneous solution approaches that of the homogeneous case when the depth of penetration in the first layer is less than the depth of the stratum. The capacitive nature of the earth due to displacement currents is shown to be significant at very high frequencies.