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The problem concerning the mutual coupling of two parallel thin-wire loop antennas in air is analyzed by formulating two coupled integral equations for the currents on the loops which are then solved by a typical Fourier series expansion method. Moment functions associated with the mutual coupling of the two loops are computed using a double Gaussian quadrature scheme. It is shown that the results as obtained from the integral equations agree with the conventional magnetic dipole approach provided that the loops are sufficiently small, and when the second loop is a perfect image of the first. For larger loops however the magnetic dipole approach cannot adequately take into account the proximity effect, since the current is assumed to be uniform. Input conductance of each loop is obtained for a wide range of separations as well as the staggering angles between the two loops. As special cases, results of a colinear and a coplanar are recovered.