  We present the evolution of the phase lags associated with the type-C QPO in
GX 339--4 during the rising phase of the 2006/2007 outburst. We find that the
phase lags at the QPO frequency are always positive (hard), and show very
different behavior between QPOs with frequencies below and above $\sim1.7$ Hz:
when the QPO frequency is below $\sim1.7$ Hz, the phase lags increase both with
QPO frequency and energy, while when the QPO frequency is above $\sim1.7$ Hz,
the phase lags remain more or less constant. When the QPO frequency is higher
than $\sim1.7$ Hz, a broad feature is always present in the lag-energy spectra
at around 6.5 keV, suggesting that the reflection component may have a
significant contribution to the phase lags. Below $\sim1.7$ Hz, the QPO rms
first decreases with energy and then turns to almost flat, while above
$\sim1.7$ Hz, the QPO rms increases with energy. During the transition from the
low-hard state to the hard-intermediate state, the second harmonic and
subharmonic of this QPO appear in the power density spectra. The
second-harmonic and subharmonic phase lags show very similar evolution with
their centroid frequencies. However, the energy dependence of the
second-harmonic and subharmonic phase lags are quite different. Our results
suggest that, at different phases of the outburst, different mechanisms may be
responsible for the phase lags of the QPO. We briefly discuss the possible
scenarios for producing the lags.
