  Charmonium and bottomonium production is studied using $\mu^+\mu^-$ data
samples collected by the CDF and D0 experiments during the 1992-96 p-pbar
collider run at the Fermilab Tevatron. The inclusive cross sections as a
function of the transverse momentum of reconstructed quarkonium states are
measured. The results are compared with theoretical predictions, which take
into account different quarkonium production mechanisms.
