  We present a comprehensive flux resolved spectral analysis of the bright
Narrow line Seyfert I AGNs, Mrk~335 and Ark~564 using observations by
XMM-Newton satellite. The mean and the flux resolved spectra are fitted by an
empirical model consisting of two Comptonization components, one for the low
energy soft excess and the other for the high energy power-law. A broad Iron
line 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 be
empirically described as $\Gamma$ = 0.6 log$_{10}$ L{$_{X}$}/L$_{Edd}$ + 3.0
for $0.005 < L{_{X}}/L_{Edd} < 0.04$. At $ L_{{X}}/L_{Edd} \sim 0.04$ the
spectral 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 result
is 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 index
variation can be empirically described as $\Gamma$ = 0.2 log$_{10}$
L$_{{X}}$/L$_{Edd}$ + 2.7 with a significantly large scatter as compared to
Mrk~335. Our results indicate that for Mrk~335, there may be accretion disk
geometry changes which lead to different parallel tracks. These changes could
be related to structural changes in the corona or enhanced reflection at high
flux levels. There does not seem to be any homogeneous or universal
relationship for the X-ray index and luminosity for different AGNs or even for
the same AGN.
