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 \sim 10 ^ { 37 } erg s ^ { -1 } and the spectrum typical for hard states of accreting black holes , and it was in an off state during the fifth one , with L \sim 10 ^ { 35 } erg s ^ { -1 } .
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 , \sim 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 RXTE /PCA during that state is found not to be intrinsic to the source but to originate mostly in the Galactic diffuse emission .