Abstract Electromagnetic response of a two-layered spherical model to a dipolar field has been calculated considering the simultaneous influences of a permeable conducting cover, magnetic permeability contrast with the surrounding medium, and radial conductivity variation inside the core. Computations have been made and representative curves are given to provide an insight of the contribution of these physical parameters. For certain conductivities of the cover, the response of the composite system has been found to decrease with increasing core-conductivity. The increase in the induction number of the covering shell makes it difficult to interpret the response data. The multifrequency response of the system exhibits two peaks which are diagnostic of the two layers.