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 $J/ψ$ 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 $χ_{c1}/χ_{c2}$ production ratio and $J/ψ$ ($ψ'$) 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.

21 pages (6 figures included)