A general cascade package is used to handle the J/psi and psi' production a
nd absorption for different E-T bins in S-U and Pb-Pb collisions. We study
the combined effect of nuclear absorption and final state interaction with
co-movers on the J/psi and psi' suppression. The experimental data of J/psi
production can be fitted for different E-T-bins in S-U collisions and for
lower E-T-bins in Pb-Pb collisions. However, psi' data for high E-T-bins in
bath S-U and Pb-Pb collisions can not be explained.