We present the first results of the spectroscopy of distant, obscured AGN as obtained with the ultra-deep (~3.3 Ms) XMM-Newton survey in the Chandra Deep Field South (CDFS). One of the primary goals of the project is to characterize the X-ray spectral properties of obscured and heavily obscured Compton-thick AGN over the range of redhifts and luminosities that are relevant in terms of their contribution to the X-ray background. The ultra-deep exposure, coupled with the XMM detectors spectral throughput, allowed us to accumulate good quality X-ray spectra for a large number of X-ray sources and, in particular, for heavily obscured AGN at cosmological redshifts. Specifically we present the X-ray spectral properties of two high-redshift - z= 1.53 and z=3.70 - sources. The XMM spectra of both are very hard, with a strong iron Kalpha line at a rest-frame energy of 6.4 keV. A reflection-dominated continuum provides the best description of the X-ray spectrum of the z=1.53 source, while the intrinsic continuum of the z=3.70 AGN is obscured by a large column N_H ~ 10^24 cm-2 of cold gas. Compton-thick absorption, or close to it, is unambiguously detected in both sources. Interestingly, these sources would not be selected as candidate Compton thick AGN by some multiwavelength selection criteria based on the mid-infrared to optical and X-ray to optical flux ratios.
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