We analytically formulate electromagnetic fields of circular loop-coilsplaced around double-structured axisymmetrical cylinders with differentelectrical conductivities and magnetic permeabilities. Formulae are given interms of conductivity, permeability and frequency in a vector potentialformalism subject to the appropriate boundary conditions on the cylindricalsurface. The impedance of the coil is numerically computed for real andimaginary parts, whose behavior is investigated in detail on the Gauss planefor various electromagnetic properties. Our model will make it clear how theimpedance of the coil depends on the conductivity and permeability insubregion of the base material, and also on the excitation frequency.