  We present a study of the polarization of the $\Upsilon(1S)$ and
$\Upsilon(2S)$ 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
$\alpha=(\sigma_{T}-2\sigma_{L})/(\sigma_{T}+2\sigma_{L})$, where $\sigma_{T}$
and $\sigma_{L}$ are the transversely and longitudinally polarized components
of the production cross section, as a function of the transverse momentum
($p_{T}^{\Upsilon}$) for the $\Upsilon(1S)$ and $\Upsilon(2S)$. Significant
$p_{T}^{\Upsilon}$-dependent longitudinal polarization is observed for the
$\Upsilon(1S)$. A comparison with theoretical models is presented.
