Orbital and Super-Orbital Periods of 1E 1740.7-2942 and GRS 1758-258

Five years of Rossi X-ray Timing Explorer (RXTE) observations of the Galactic black-hole candidates 1E 1740.7-2942 and GRS 1758-258 show a periodic modulation with amplitude 3-4% in each source at 12.73 +/- 0.05 dy and 18.45 +/- 0.10 dy, respectively. We interpret the modulations as orbital, suggesting that the objects have red-giant companions. Combining the RXTE data with earlier data (Zhang, Harmon & Liang 1997) from the Burst and Transient Source Experiment on the Compton Gamma-Ray Observatory, we find a long period or quasi-period of about 600 dy in 1E 1740.7-2942, and a suggestion of a similar 600-dy period in GRS 1758-258. These timescales are longer than any yet found for either precessing systems like Her X-1 and SS 433 or binaries like LMC X-3 and Cyg X-1 with more irregular long periods.