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.