  The long term X-ray spectral variability of ten active galactic nuclei (AGN)
shows a positive spectral index-flux correlation for each object (Sobolewska &
Papadakis 2009). An inner advection dominated accretion flow (ADAF) may connect
to a thin disc/corona at a certain transition radius, which are responsible for
hard X-ray emission in AGN. The ADAF is hot and its X-ray spectrum is hard,
while the corona above the disc is relatively cold and its X-ray spectrum is
therefore soft. The radiation efficiency of the ADAF is usually much lower than
that of the thin disc. The increase of the transition radius may lead to
decreases of the spectral index (i.e., a hard spectrum) and the X-ray
luminosity even if the accretion rate is fixed, and vice versa. We propose that
such X-ray variability is caused by the change of the transition radius. Our
model calculations can reproduce the observed index-flux correlations, if the
transition radius fluctuates around an equilibrium position, and the radiation
efficiency of ADAFs is {\guillemotright} 5 per cent of that for a thin disc.
The average spectral index-Eddington ratio correlation in the AGN sample can
also be reproduced by our model calculations, if the equilibrium transition
radius increases with decreasing mass accretion rate.
