Prompt gluons are an additional source for charmonium suppression in nuclea
r collisions, in particular for nucleus-nucleus collisions. These gluons ar
e radiated as bremsstrahlung in N-N collisions and interact inelastically w
ith the charmonium states while the nuclei still overlap. The spectra and m
ean number [n(g)] of the prompt gluons are calculated perturbatively and th
e inelastic cross section sigma(abs)(Psi g) is estimated. The integrated cr
oss sections sigma(AB --> J/phi X) for p-A and A-B collisions and the depen
dence on transverse energy for S-U and Pb-Pb can be described quantitativel
y with some adjustment of one parameter [n(g)] sigma(abs)(Psi g).