In this paper we report on the spectral evolution of 4U 1608-522 performed as part of the long Galactic Bulge monitoring with INTEGRAL. The data set include the April 2005 outburst. BeppoSAX archival data (two observations, in 1998 and 2000) have been also analysed and compared with the INTEGRAL ones. Three different spectral states have been identified from the hard Color-Intensity diagram derived from INTEGRAL: the canonical Hard and Soft as well as an Intermediate state. The hard state spectrum is well described by a weak black body component plus a Comptonised plasma component with high electron temperature (kTe~60 keV) extending up to 200 keV without any additional cut-off. The soft spectra are characterized by a cold Comptonised plasma (kTe= 2-3 keV, and 7 keV for the intermediate state) and a strong disk black body component. A reflection component, indicating reflection of the X-ray radiation from the accretion disc, is also present in the soft state revealed by BeppoSAX in 1998. The 2000 BeppoSAX observation revealed the source in quiescent state modelled by a neutron star atmosphere (assuming a neutron star with radius 10 km and mass 1.4 Msun) with an effective temperature, kTeff of 0.1 keV plus a power law component with Gamma~3 detected for the first time for this source. This spectrum can also be modelled with a simple black body compatible with emission originating from a small fraction of the NS surface of radius of 0.4 km.
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