  We report on X-ray observations of the black-hole candidate GX 339-4 during
its 2006/2007 outburst. The hardness-intensity diagram of all RXTE/PCA data
combined shows a q-shaped track similar to that observed in previous outbursts.
The evolution through the HID suggests that in the early phase of the outburst
the source underwent a sequence of state transitions, from the hard to the soft
state, which is supported by our timing analysis. Broadband (4-200 keV)
spectra, fitted with an exponentially cutoff powerlaw, show that the hard
spectral component steepens during the transition from the hard to the soft
state. The high-energy cutoff decreased monotonically from 120 to 60 keV during
the brightening of the hard state, but increased again to 100 keV during the
softening in the hard intermediate state. In the short-lived soft intermediate
state the cutoff energy was ~ 130 keV, but was no longer detected in the soft
state. This is one of the first times that the high-energy cut-off has been
followed in such detail across several state transitions. We find that in
comparison to several other spectral parameters, the cut-off energy changes
more rapidly, just like the timing properties. The observed behaviour of the
high energy cutoff of GX 339-4 is also similar to that observed with
RXTE-INTEGRAL-Swift during the 2005 outburst of GRO J1655-40. These results
constitute a valuable reference to be considered when testing theoretical
models for the production of the hard component in these systems.
