We use recent data obtained by three (OSSE, BATSE, and COMPTEL) of four ins
truments on board the Compton Gamma Ray Observatory (CGRO) to construct a m
odel of Cyg X-1 that describes its emission in a broad energy range, from s
oft X-rays to MeV gamma-rays, self-consistently. The gamma-ray emission is
interpreted to be the result of Comptonization, bremsstrahlung, and positro
n annihilation in a hot, optically thin, and spatially extended region surr
ounding the whole accretion disk. For the X-ray emission, a standard corona
-disk model is applied. We show that the Cyg X-1 spectrum accumulated by th
e CGRO dinstruments during a similar to 4 year time period between 1991 and
1995, as well as the HEAO 3 gamma(1) and gamma(2) spectra, can be well rep
resented by our model. The derived parameters match the observational resul
ts obtained from X-ray measurements.