The Oriented Scintillation Spectrometer Experiment on the Compton Gamma Ray Observatory has carried out spectral and timing observations of Galactic black hole candidates GX 339-4 and Cyg X-1. GX 339-4 was observed as a target of opportunity in 1991 September, in response to the outburst reported by BATSE and SIGMA. The source was detected from 50 to 400 keV, at a level relative to the Crab of ∼30%. During a followup observatio. n made in 1991 November, the intensity of the source below 100 keV had dropped by nearly two orders of magnitude, and it was no longer detected above 100 keV. The observations of Cyg X-1 were made during three different observing periods between 1991 June and November. The OSSE time-averaged spectrum of Cyg X-1 is about 10 times brighter than that of GX 339-4, but remarkably similar in shape over the energy range in which both are detected. No significant emission is seen above about 1 MeV, and there is no evidence for any bumps or narrow lines near 0.511 MeV. The spectra of both sources are decribed reasonably well by a Comptonization model.