  We analyze charmonium and bottomonium production at fixed target experiments.
We find that inclusion of color octet production channels removes large
discrepancies between experiment and the predictions of the color singlet model
for the total production cross section. Furthermore, including octet
contributions accounts for the observed direct to total $J/\psi$ production
ratio. As found earlier for photo-production of quarkonia, a fit to fixed
target data requires smaller color octet matrix elements than those extracted
from high-$p_t$ production at the Tevatron. We argue that this difference can
be explained by systematic differences in the velocity expansion for collider
and fixed-target predictions. While the color octet mechanism thus appears to
be an essential part of a satisfactory description of fixed target data,
important discrepancies remain for the $\chi_{c1}/\chi_{c2}$ production ratio
and $J/\psi$ ($\psi'$) polarization. These discrepancies, as well as, the
differences between pion and proton induced collisions emphasize the need for
including higher twist effects in addition to the color octet mechanism.
