  The hadroproduction of direct J/Psi in the framework of the
k_\perp-factorization approach is studied. The color-singlet contribution is
essentially larger than in the collinear approach but is still an order of
magnitude below the data. The deficit may be well described by the color octet
contribution with the value of the matrix element <0|O^{J/\Psi}_8(^3S_1)|0>
substantially decreased in comparison with the fits in the collinear
factorization. This should lead to a reduction of the large transverse
polarization, predicted in the collinear approach.
