The two neutrino double-beta decay of Xe, with a half-life of y, is among the rarest nuclear processes ever directly observed. The hypothesized neutrinoless double-beta decay of Xe, which nEXO aims to observe, is expected to be that much rarer, with a half-life of at least y at 90% C.L. Sufficient suppression of backgrounds is, therefore, crucial to making a discovery possible. The bulk of these backgrounds for nEXO are expected to result from radioactivity in the detector components. Reducing this background contribution to a sufficiently low level requires a comprehensive material screening program. This poster describes the techniques the nEXO Collaboration employs, built on the highly successful program developed by EXO-200, in the assay of candidate materials for nEXO components. A summary of recently released results of these efforts will also be presented.