  We analyse five observations of the X-ray binary GX 339-4 by the soft
gamma-ray OSSE detector on board CGRO simultaneous with either Ginga or RXTE
observations. The source was bright during four of them, with the luminosity of
L ~ 10^{37} erg/s and the spectrum typical for hard states of accreting black
holes, and it was in an off state during the fifth one, with L ~ 10^{35} erg/s.
Our broad-band spectral fits show the mean electron energy of electrons in the
Comptonizing plasma decreasing with increasing luminosity within the hard
(bright) state. For the observation with the best statistics at soft
gamma-rays, approximately 1/4 of energy in the Comptonizing plasma is probably
carried by non-thermal electrons. Then, considering the efficiency of
Comptonized hybrid synchrotron emission allows us to obtain an upper limit on
the strength of the magnetic field in the X-ray source. Furthermore, this
synchrotron emission is capable of producing the optical spectrum observed in
an optically-high state of GX 339-4. In the off state, the hard X-ray spectrum
is consistent with being dominated by bremsstrahlung. The unusually strong Fe K
alpha line observed by the PCA during that state is found not to be intrinsic
to the source but to originate mostly in the Galactic diffuse emission.
