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We present the first broadband X-ray observations of four Giga-Hertz PeakedSpectrum (GPS) radio galaxies at redshift <~1 performed by Chandra andXMM-Newton. These observations more than double the number of members of thisclass with measured spectra in hard (E > 2 keV) X-rays. All sources weredetected. Their radio-to-X-ray spectral energy distributions are similar,except for PKS0941-080, which is X-ray under-luminous by about two orders ofmagnitude. The comparison between the full sample of GPS galaxies withmeasurements in hard X-rays and a control sample of radio galaxies rules outintrinsic X-ray weakness as causing a lower detection rate of GPS sources inX-ray surveys. Four out of seven GPS galaxies exhibit high X-ray columndensities, whereas for the remaining three this measurement is hampered by thepoor spectral statistics. Bearing in mind the low number statistics in both theGPS and the control sample, the average column density measured in GPS galaxiesis larger than in FRI or Broad Line Region FR II radio galaxies, but consistentwith that measured in High-Excitation FRII galaxies. This leads to a locationthe absorbing gas in an obscuring ``torus'', which prevents us from observingthe nuclear region along lines-of-sight perpendicular to the radio axis. Thisinterpretation is supported by the discovery of rapid (timescale ~1000 s) X-rayvariability in the GPS galaxy COINSJ0029+3456, and by an almostorder-of-magnitude difference between the HI column density measured in radioand X-rays in PKS0500+019.Comment: Accepted for publication in Astronomy and Astrophysics. 11 pages, 8  figures. Minor editorial change

A hard X-ray view of giga-hertz peaked spectrum radio galaxies