We study the flux-flux plots (FFPs) of the Seyfert galaxy SWIFT J2127.4+5654 which was observed simultaneously by XMM-Newton and NuSTAR. The 0.7-2 keV FFPs show a non-linear behaviour, while they are well fitted by a straight line, in the ∼ 2−40 keV range. Without any additional modelling, this result strongly suggests that neither absorption nor spectral slope variations can contribute significantly to the observed variability above 2 keV (on time scales 5 days, at least). The FFP method is capable of separating the variable and the constant X-ray spectral components in this source. We found that the low-, average-and high-flux spectra of the variable components are consistent with a power law varying in normalisation only plus a relativistic reflection component varying simultaneously with the continuum. At low energies, we identify an additional variable component, consistent with a neutral absorber with a variable covering fraction. We also detect two spectral components whose fluxes remain constant over the duration of the observations. These components can be well described by a blackbody emission of kT BB ∼ 0.18 keV, dominating at soft X-rays, and a reflection component from neutral material. The spectral model resulting from the FFP analysis can fit well the energy spectra of the source. We suggest that a combined study of FFPs and energy spectra in the case of X-ray bright and variable Seyferts can identify, unambiguously, the various spectral components, and can lift the degeneracy that is often observed within different models fitting equally well time-averaged spectra of these objects.