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 ( similar to the κ and λ classes in GRS 1915+105). 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. Using joint spectral analysis of peak and dip spectra with a variable emission component, we verify that the variable component is consistent with p−free disc blackbody and its spectral parameters are similar to that found from the difference spectral analysis. In contrast, we show that for oscillations in the θ class where soft dips are observed, the difference spectra cannot be similarly fitted. 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 of ∼ 10 variation seen between the peak and dip levels. (MP) days, makes GRS 1915+105 unique with respect to other micro-quasars. These drops are most prominent in κ, λ and ρ classes and they are simultaneous with spectral hardening by a couple of factors (Yadav et al. 1999;Belloni et al. 2000;Rao et al. 2000;Naik et al. 2002a).Several attempts have been made to model the spectra of such fluctuations by assuming that the energy spectra at the base/persistent flux level of the fluctuation are consistent with the low hard state (L bol /LEDD ∼ 0.05−0.2) while energy spectra at the peak flux level are consistent with