We analytically formulate electromagnetic fields of circular loop-coils placed around double-structured axisymmetrical cylinders with different electrical conductivities and magnetic permeabilities. Formulae are given in terms of conductivity, permeability and frequency in a vector potential formalism subject to the appropriate boundary conditions on the cylindrical surface. The impedance of the coil is numerically computed for real and imaginary parts, whose behavior is investigated in detail on the Gauss plane for various electromagnetic properties. Our model will make it clear how the impedance of the coil depends on the conductivity and permeability in subregion of the base material, and also on the excitation frequency.