  In June 2015, the source V404 Cygni (= GS2023+38) underwent an extraordinary
outburst. We present the results obtained during the first revolution dedicated
to this target by the INTEGRAL mission, and focus on the spectral behavior in
the hard X-ray domain, using both SPI and IBIS instruments. The source exhibits
extreme variability, and reaches fluxes of several tens of Crab. However, the
emission between 20 and 650 keV can be understood in terms of two main
components, varying on all the observable timescales, similar to what is
observed in the persistent black hole system Cyg X-1. The low energy component
(up to ~ 200 keV) presents a rather unusual shape, probably due to the
intrinsic source variability. Nonetheless, a satisfactory description is
obtained with a Comptonization model, if an unusually hot population of seed
photons ($kT_0$ ~ 7 keV) is introduced. Above this first component, a clear
excess extending up to 400-600 keV leads us to investigate a scenario where an
additional (cutoff) power law could correspond to the contribution of the jet
synchrotron emission, as proposed in Cyg X-1. A search for an annihilation
feature did not provide any firm detection, with an upper limit of 2 x $10^{-4}
ph/cm^2 s$ (2 \sigma) for a narrow line centered at 511 keV, on the averaged
obtained spectrum.
