Analytical solution for the change in impedance of a coil located inside or outside a multilayer conducting tube is obtained in the present paper. The electric conductivity and magnetic permeability of conducting cylindrical layers of the tube are assumed to be power functions of the radial coordinate. The change in impedance is expressed in terms of improrer integral containing Bessel functions. Other analytical solutions are suggested in the paper. Three examples are discussed in detail: (a) a coil inside an infinite cylindrical layer, (b) a coil inside a two-layer tube, and (c) a coil outside a two-layer tube.