  The microquasar GX 339-4, known to exhibit powerful compact jets that
dominate its radio to near-infrared emission, entered an outburst in 2010 for
the fifth time in about fifteen years. An extensive radio to X-ray
multi-wavelength campaign was immediately triggered, and we report here on
ESO/FORS2+ISAAC optical and near-infrared spectroscopic observations, supported
by ATCA radio and RXTE/Swift X-ray quasi-simultaneous data. GX 339-4 was
observed at three different epochs, once in the soft state and twice in the
hard state. In the soft state, the optical and near-infrared continuum is
largely consistent with the Raleigh-Jeans tail of a thermal process. As an
explanation, we favour irradiation of the outer accretion disc by its inner
regions, enhanced by disc warping. An excess is also present at low
frequencies, likely due to a M subgiant companion star. During the first hard
state, the optical/near-infrared continuum is well-described by the optically
thin synchrotron emission of the compact jet combined with disc irradiation and
perhaps another component peaking in the ultraviolet. The spectral break where
the jet transits from the optically thick to thin regimes, located below
1.20e14 Hz, is not detected and the extension of the optically thin synchrotron
is consistent with the 3-50 keV spectrum. In contrast, the emission during the
second hard state is more difficult to understand and points toward a more
complex jet continuum. In both cases, the near-infrared continuum is found to
be variable at timescales at least as short as 20 s, although these
variabilities are smoothed out beyond a few hundred seconds. This implies rapid
variations - in flux and frequency - of the location of the spectral break,
i.e. dramatic short timescale changes of the physical conditions at the base of
the jet, such as the magnetic field and/or the base radius.
