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We present a comprehensive flux resolved spectral analysis of the brightNarrow line Seyfert I AGNs, Mrk~335 and Ark~564 using observations byXMM-Newton satellite. The mean and the flux resolved spectra are fitted by anempirical model consisting of two Comptonization components, one for the lowenergy soft excess and the other for the high energy power-law. A broad Ironline and a couple of low energies edges are required to explain the spectra.For Mrk~335, the 0.3 - 10 keV luminosity relative to the Eddington value,L{$_{X}$}/L$_{Edd}$, varied from 0.002 to 0.06. The index variation can beempirically described as $\Gamma$ = 0.6 log$_{10}$ L{$_{X}$}/L$_{Edd}$ + 3.0for $0.005 < L{_{X}}/L_{Edd} < 0.04$. At $ L_{{X}}/L_{Edd} \sim 0.04$ thespectral index changes and then continues to follow $\Gamma$ = 0.6 log$_{10}$L$_{{X}}$/L$_{Edd}$ + 2.7, i.e. on a parallel track. We confirm that the resultis independent of the specific spectral model used by fitting the data in the 3- 10 keV band by only a power-law and an Iron line. For Ark~564, the indexvariation can be empirically described as $\Gamma$ = 0.2 log$_{10}$L$_{{X}}$/L$_{Edd}$ + 2.7 with a significantly large scatter as compared toMrk~335. Our results indicate that for Mrk~335, there may be accretion diskgeometry changes which lead to different parallel tracks. These changes couldbe related to structural changes in the corona or enhanced reflection at highflux levels. There does not seem to be any homogeneous or universalrelationship for the X-ray index and luminosity for different AGNs or even forthe same AGN.

Relationship between X-ray spectral index and X-ray Eddington ratio for Mrk 335 and Ark 564