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No optical counterparts of the Galactic Center hard X-ray sources 1E1740.7-2942 and GRS 1758-258 have so far been found even in the deepest IR imaging. We show that the newest optical/IR upper limits in I, K, and L bands, when plotted on a H-R diagram by adopting reasonable extinction, severely constraints the luminosity and spectral type of the optical counterparts. \newline \indent Hard X-ray monitoring by GRANAT/Sigma has shown long-term, large amplitude variability on a time scale of 1-2 years. It cannot be due to orbital modulation of the accretion flow. We discuss the possibility of producing such a long-term variability in a LMXB, in analogy to similar variability observed in some CVs. It is also possible that these two gamma-ray sources are powered by accretion directly from the ISM. The possible mechanisms of producing the variability in Bondi-Hoyle accretion are discussed.
