  We present X-ray/gamma-ray spectra of Cyg X-1 observed during the transition
from the hard to the soft state and in the soft state by ASCA, RXTE and OSSE in
1996 May and June. The spectra consist of a dominant soft component below ~2
keV and a power-law-like continuum extending to at least ~800 keV. We interpret
them as emission from an optically-thick, cold accretion disc and from an
optically-thin, non-thermal corona above the disc. A fraction f ~ 0.6 of total
available power is dissipated in the corona. We model the soft component by
multi-colour blackbody disc emission taking into account the torque-free
inner-boundary condition. If the disc extends down to the minimum stable orbit,
the ASCA/RXTE data yield the most probable black hole mass of about 10 solar
masses and an accretion rate about 0.5 L_E/c^2, locating Cyg X-1 in the soft
state in the upper part of the stable, gas-pressure dominated, accretion-disc
solution branch. The spectrum of the corona is well modelled by repeated
Compton scattering of seed photons from the disc off electrons with a hybrid,
thermal/non-thermal distribution. The electron distribution can be
characterized by a Maxwellian with an equilibrium temperature of kT ~ 30--50
keV and a Thomson optical depth of ~0.3 and a quasi-power-law tail. The
compactness of the corona is between 2 and 7, and a presence of a significant
population of electron-positron pairs is ruled out. We find strong signatures
of Compton reflection from a cold and ionized medium, presumably an accretion
disc, with an apparent reflector solid angle ~0.5--0.7. The reflected continuum
is accompanied by a broad iron K-alpha line.
