The paramagnetic resonance spectrum of Cr3+ pairs in ruby which interact via exchange and dipolar forces have been studied at 15.74 kMc in the temperature range 1.2° to 700°K. Theoretical analysis predicts and experiments confirm that relatively distant neighbors with negligible exchange coupling give rise to resonance lines which cluster around isolated Cr3+ ion lines. Spin pairs coupled through exchange forces large as compared to the Zeeman or crystalline field energies give rise to lines that cluster around magnetic field values different from those for isolated Cr3+ lines. Exact calculations on an IBM 704 computer are used to assign lines in a given cluster to various neighbor pairs. This assignment together with the temperature dependence of the line intensities are used to determine the exchange forces. For nearest neighbors the exchange constant is 390±50 cm−1 while the 3rd through 11th neighbor shells have exchange interactions of order 1 cm−1. Spin-lattice relaxation is discussed for pairs coupled through anisotropic exchange or weak isotropic exchange forces.