  Prompt gluons are an additional source for charmonium suppression in nuclear
collisions, in particular for nucleus-nucleus collisions. These gluons are
radiated as bremsstrahlung in N-N collisions and interact inelastically with
the charmonium states while the nuclei still overlap. The spectra and mean
number <n_g> of the prompt gluons are calculated perturbatively and the
gluon-Psi inelastic cross section is estimated. The integrated cross sections
for AB --> J/Psi (Psi')X for p-A and A-B collisions and the dependence on
transverse energy for S-U and Pb-Pb can be described quantitatively with some
adjustment of one parameter <n_g>\sigma(gPsi).
