The paper studies the so-called coaxial overhead transmission lines. The concentric phases are considered. The mathematical analysis for voltage and current is presented. The telegraphic equations of the double circuit power lines with the mutual effect between circuits are introduced. The condition for single circuit transmission line is checked. The mutual effect between both circuits is studied on the basis of the ratio between the two currents of both circuits. The appeared phase shift between the two vectors of currents is inserted in the investigation. The magnetic field intensity at an external point of a line is mathematically expressed. Its value is approximated for the purpose of zero mutual inductance between phases of the same circuit. The mutual inductance between the two nearest groups of phases due to the linkage flux for the studied line is formulated. Its dependency on the distance from the phases as well as on the ratio of currents of both circuits is analysed. Then, the effect of phase shift on the mutual inductance is investigated. An idea for the control of the ratio between currents of both circuits of a line is presented.