  We present the X-ray analysis of the most luminous obscured active galactic
nuclei (AGN) inside local ultraluminous infrared galaxies (ULIRGs). Our sample
consists of ten sources, harbouring AGN components with estimated luminosity in
excess of ~10^12 L_sun and yet unidentified at optical wavelengths because of
their large obscuration. According to the Chandra and XMM-Newton spectra, only
in two cases out of ten clear AGN signatures are detected at 2-10 keV in the
shape of reflected emission. The X-ray flux from the starburst (SB) components,
instead, is always broadly consistent with the expectations based on their IR
emission. The most convincing explanation for the missing AGN detections is
therefore the Compton-thickness of the X-ray absorber. In general, the
combination of our mid-IR and X-ray spectral analysis suggests that the
environment surrounding the AGN component in ULIRGs is much richer in gas and
dust than in ordinary active galaxies, and the degree of AGN absorption can be
tentatively related to the SB intensity, indicating a strong interaction
between the two processes and supporting the ULIRG/quasar evolutionary scheme.
