  The Neutrino Experiment with a Xenon TPC (NEXT) is intended to investigate
the neutrinoless double beta decay of 136Xe, which requires a severe
suppression of potential backgrounds. An extensive screening and material
selection process is underway for NEXT since the control of the radiopurity
levels of the materials to be used in the experimental set-up is a must for
rare event searches. First measurements based on Glow Discharge Mass
Spectrometry and gamma-ray spectroscopy using ultra-low background germanium
detectors at the Laboratorio Subterr\'aneo de Canfranc (Spain) are described
here. Activity results for natural radioactive chains and other common
radionuclides are summarized, being the values obtained for some materials like
copper and stainless steel very competitive. The implications of these results
for the NEXT experiment are also discussed.
