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We present a study of the polarization of the Ү(1S) and Ү(2S) states using a 1.3 fb-1 data sample collected by the D0 experiment in 2002–2006 during run II of the Fermilab Tevatron Collider. We measure the polarization parameter α = (σT - 2σL), where σT and σL are the transversely and longitudinally polarized components of the production cross section, as a function of the transverse momentum (pTҮ) for the Ү(1S) and Ү(2S). Significant pTҮ-dependent longitudinal polarization is observed for the Ү(1S). A comparison with theoretical models is presented.