  Using the flux resolved spectroscopy for the first time, we analyse the
RXTE/PCA data of the black hole X-ray binaries GRS 1915+105 and IGR
J17091-3624, when both sources show large amplitude, quasi-regular oscillations
in 2.0-60.0 keV X-ray light curves. For different observations, we extract
spectra during the peak (spectrally soft) and dip (spectrally hard) intervals
of the oscillation, and find that their spectra are phenomenologically complex,
requiring at least two distinct spectral components. Besides a thermal
Comptonization component, we find that the disc emission is better modelled by
an index-free multicolour disc blackbody component (p-free disc model) rather
than that from a standard accretion disc. While the peak and dip spectra are
complex, remarkably, their difference spectra constructed by treating dip
spectra as the background spectra of the peak spectra, can be modelled as a
single p-free disc component. Moreover, the variability at different
time-scales and energy bands of the peak flux level is always greater than or
equal to the variability of the dip flux level, which strengthens the
possibility that the peak flux level may be due to an independent spectral
component added to the dip one. We also verify it using joint spectral analysis
of peak and dip spectra with a variable emission component. Our result
substantiates the standard hypothesis that the oscillations are due to the
limit cycle behaviour of an unstable radiation pressure dominated inner disc.
However, in this interpretation, the flux variation of the unstable disc can be
several order of magnitudes as expected from some theoretical simulations and
need not be fine tuned to match the factor ~10 variation seen between the peak
and dip levels.
