The ``Neutrino Experiment with a Xenon Time-ProjectionChamber'' (NEXT) is intended to investigate the neutrinoless doublebeta decay of 136Xe, which requires a severe suppression ofpotential backgrounds. An extensive screening and material selectionprocess is underway for NEXT since the control of the radiopuritylevels of the materials to be used in the experimental set-up is amust for rare event searches. First measurements based on GlowDischarge Mass Spectrometry and gamma-ray spectroscopy usingultra-low background germanium detectors at the LaboratorioSubterr'aneo de Canfranc (Spain) are described here. Activity resultsfor natural radioactive chains and other common radionuclides aresummarized, being the values obtained for some materials like copperand stainless steel very competitive. The implications of theseresults for the NEXT experiment are also discussed.
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