A theory for two identical square loop antennas driven in the zeroth-phase sequence (voltages in phase at all four corners) and the second-phase sequence (voltages in and out of phase at the corners) is formulated. Eight independent integral equations are obtained. They are solved individually by the method of iteration, and first-order formulas are obtained for the current distributions and driving point impedances. For each phase sequence, the sum of the symmetrical and antisymmetrical impedances gives the self-impedance and the difference between them gives the mutual impedance. Self and mutual impedances are also obtained for a superposition of the two phase sequences.