  We report on the June 2000 long (100 ks) BeppoSAX exposure that has unveiled
above 10 keV a new very high energy component of the X-ray spectrum of Eta Car
extending to at least 50 keV. We find that the 2-150 keV spectrum is best
reproduced by a thermal + non-thermal model. The thermal component dominates
the 2-10 keV spectral range with kT_h=5.5 +/- 0.3 keV and log NH_h=22.68 +/-
0.01. The spectrum displays a prominent iron emission line centred at 6.70 keV.
Its equivalent width of 0.94 keV, if produced by the thermal source, gives a
slightly sub-solar iron abundance ([Fe/H]=-0.15 +/- 0.02).
  The high energy tail above 10 keV is best fitted by a power law with a photon
index of 2.42 +/- 0.04. The integrated 13-150 keV luminosity of ~12 L-sun is
comparable to that of the 2-10 keV thermal component. The present result can be
explained, in the Eta Car binary star scenario, by Comptonisation of low
frequency radiation by high energy electrons, probably generated in the
colliding wind shock front, or in instabilities in the wind of the S Dor
primary star. It is possible that the high energy tail had largely weakened
near the minimum of the 5.53 yr cycle. With respect to the thermal component,
it probably has a longer recovering time like that of the highest excitation
optical emission lines. Both features can be associated with the large
absorption measured by BeppoSAX at phase 0.05.
