Abstract – In the present paper the change in impedance per unit length of a double conductor line formed by two parallel wires with alternating current is calculated. The double conductor line is located above a two-layer medium. The magnetic permeability and electric conductivity of the upper layer are exponential functions of the vertical coordinate. The properties of the lower layer are assumed to be constant. The solution is obtained in closed form by means of the Fourier sine and cosine integral transform and is expressed in terms of improper integral containing Bessel functions.