We report the experimental observation of an EPR spectral manifestation of spin exchange frequencies, ωex, larger than the 15N hyperfine separation, A0, predicted 50 years ago but previously not observed. For spectra with ωex/γA0 < 1, where γ is the gyromagnetic ratio of the electron, the spectrum consists of two "normal" spin modes each with one absorption and one dispersion component separated by Aabs < A0. Aabs decreases with ωex. In stark contrast, when ωex/γA0 > 1, the spectrum consists of two absorption spin modes, one of which is negative (emissive). We show that the experimental behavior of the spin modes agrees with theory: (a) the doubly integrated intensity of the first-derivative spectra remains constant because the increased intensity of the positive spin mode minus the negative emissive mode remains constant; (b) the value of the spin exchange rate constant Kex = ωex/C, where C is the molar concentration, is continuous through ωex/γA0 = 1.