We have used observations from CGRO to study the variation in the MeV emission of Cygnus X-1 between its low and high X-ray states. These data provide a measurement of the spectral variability above 1 MeV. The high state MeV spectrum is found to be much harder than that of the low state MeV spectrum. In particular, the power-law emission seen at hard X-ray energies in the high state spectrum (with a photon spectral index of 2.6) is found to extend out to at least 5 MeV, with no evidence for any cutoff. Here we present the data and describe our efforts to model both the low state and high state spectra using a hybrid thermal/nonthermal model in which the emission results from the Comptonization of an electron population that consists of both a thermal and nonthermal component. ©2001 American Institute of Physics.