  We aim to study the variability properties of bright hard X-ray selected
Active Galactic Nuclei (AGN) with redshift between 0.3 and 1.6 detected in the
Chandra Deep Field South (XMM-CDFS) by a long XMM observation. Taking advantage
of the good count statistics in the XMM CDFS we search for flux and spectral
variability using the hardness ratio techniques. We also investigated spectral
variability of different spectral components. The spectra were merged in six
epochs (defined as adjacent observations) and in high and low flux states to
understand whether the flux transitions are accompanied by spectral changes.
The flux variability is significant in all the sources investigated. The
hardness ratios in general are not as variable as the fluxes. Only one source
displays a variable HR, anti-correlated with the flux (source 337). The
spectral analysis in the available epochs confirms the steeper when brighter
trend consistent with Comptonisation models only in this source. Finding this
trend in one out of seven unabsorbed sources is consistent, within the
statistical limits, with the 15 % of unabsorbed AGN in previous deep surveys.
No significant variability in the column densities, nor in the Compton
reflection component, has been detected across the epochs considered. The high
and low states display in general different normalisations but consistent
spectral properties. X-ray flux fluctuations are ubiquitous in AGN. In general,
the significant flux variations are not associated with a spectral variability:
photon index and column densities are not significantly variable in nine out of
the ten AGN over long timescales (from 3 to 6.5 years). The photon index
variability is found only in one source (which is steeper when brighter) out of
seven unabsorbed AGN. These results are consistent with previous deep samples.
