By means of a straightforward boundary-value treatment, a solution is obtained for the electromagnetic response of a homogeneous sphere enclosed by a uniform spherical shell. A quasi-static assumption is invoked at the outset because attention is directed to slowly varying fields. Expressions are derived for the 'in-phase' and 'quadrature phase' response of the induced multipoles. These are a function of the radius, conductivity, and permeability of the core, and the radius, conductivity, and thickness of the shell. Some numerical results for the nonpermeable case indicate that the dependence of the dipole response on the normalized core radius is altered significantly by the presence of the shell. On the other hand, the ability to detect the presence of the core is not greatly impaired.