  We consider stochastic particle acceleration in plasmas around stellar mass
black holes to explain the emissions above 1 MeV from Galactic black hole
candidates. We show that for certain parameter regimes, electrons can overcome
Coulomb losses and be accelerated beyond the thermal distribution to form a new
population, whose distribution is broad and usually not a power law; the peak
energy of the distribution is determined by the balance between acceleration
and cooling, with particles piling up around it. Radiation by inverse Compton
scattering off the thermal (from background) and non-thermal (produced by
acceleration) particles can in principle explain the hard X-ray to gamma-ray
emissions from black hole candidates. We present model fits of Cyg X-1 and GRO
J0422 in 50 keV -- 5 MeV region observed with OSSE and COMPTEL.
