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Multiple magnetic resonance lines have been observed for H1, F19, and P31 nuclei in compounds such as PH3, PF3, F2PO(OH), and BrF5, in the liquid state. The multiplets consisted of two to seven equally spaced narrow components, symmetrically placed about a central frequency, and with splittings from 0.02 to 0.8 gauss. These multiplets arise from a new variety of interaction among the nuclear moments in a molecule. Resonance lines were found to be multiple either when a nucleus interacted with a different species of nucleus or when there was interaction between nuclei of the same species with resonance frequencies separated by a chemical shift. No compounds exhibited multiplets attributable to interactions among structurally equivalent nuclei. Nor were multiplets caused by nuclei whose electric quadrupole moments were coupled to a direction fixed in the molecule. The number and relative intensities of the components of a multiplet were determined by the number and statistical weights of the various nuclear spin orientations of the nuclei causing the splitting. In a given molecule, the ratio of the multiplet splittings of the two different resonance lines was inversely proportional to the ratio of the gyromagnetic ratios of the interacting nuclei. The splittings were independent of applied magnetic field at 4180 and 6365 gauss; they were independent of temperature over ranges from 55°C to −130°C. In PF5, the one gas examined, the splitting of the doublet fluorine resonance was the same in the gas and liquid phases; also, the doublet was demonstrated to arise from coupling with the phosphorus nucleus, rather than from a chemical shift between the resonances from the apex and meridian fluorines in the bipyramidal structure, as proposed earlier. All of the above characteristics are accounted for theoretically by assuming the magnetic nuclei interact via magnetic fields inside the molecule. The qualitative aspects are predicted by coupling of the form A12μ1·μ2 between the nuclear moments μ1 and μ2. The coupling constant A12 depends upon the detailed mechanism, which must involve the molecular electrons. Second-order perturbation theory was used to calculate the relative magnitudes of coupling via the electron orbital and the electron spin magnetic moments. The electron spin mechanism was found to give splittings ten to twenty times the orbital. Approximate calculation of the electron spin mechanism in several simpler cases gave good agreement with experiment. The influence upon the splittings of electric quadrupole coupling and spin-lattice relaxation was considered and is discussed briefly.