Cygnus X-1 and the gamma-ray transients GRO J0422+32 and GRO J1719 − 24 displayed similar spectral properties when they underwent transitions between the high and low gamma-ray (30 keV to few MeV) intensity states. When these sources were in the high γ-ray intensity state (γ 2 , for Cygnus X-1), their spectra featured two components: a Comptonized shape below 200-300 keV with a soft power-law tail (photon index >3) that extended to ∼1 MeV or beyond. When the sources were in the low-intensity state (γ 0 , for Cygnus X-1), the Comptonized spectral shape below 200 keVtypically vanished and the entire spectrum from 30 keV to ∼1 MeV can be characterized by a single power law with a relatively harder photon index ∼ 2 − 2.7. Consequently the high-and low-intensity gammaray spectra intersect, generally in the ∼400 keV -∼1 MeV range, in contrast to the spectral pivoting seen previously at lower (∼10 keV) energies. The presence of the power-law component in both the high-and low-intensity gamma-ray spectra strongly suggests that the non-thermal process is likely to be at work in both the high and the low-intensity situations. We have suggested a possible scenario (Ling & Wheaton, 2003), by combining the ADAF model of Esin et al. (1998) with a separate jet region that produces the non-thermal gamma-ray emission, and which explains the state transitions. Such a scenario will be discussed in the context of the observational evidence, summarized above, from the database produced by EBOP, JPL's BATSE earth occultation analysis system.