The paper presents a theoretical and numerical computation of the quasi-static transient response of the multipoles induced in a two-layer spherical model by a dipolar field. The sphere and its surrounding shell are of arbitrary conductivities and magnetic permeabilities. The shell, in general, acts as a screen. The early stages of the decay curves are influenced only by the physical and geometrical parameters of the shell. For inner spheres that are good conductors, the latter part of the decay curves are governed predominantly by the physical and geometrical parameters of the core.