In Z(O) decay into prompt charmonium, i.e. charmonium not originating
from B-meson decays, the most important contribution is expected to co
me from colour-octet mechanisms. However, previous fixed-order calcula
tions of the colour-octet contribution contain large logarithms which,
in a more complete treatment, should be resummed to all orders. We st
udy this resummation by using a Monte Carlo QCD cascade model and find
that the fixed-order colour-octet result is diminished by 15%. We com
pare the Monte Carlo calculations with results obtained by using analy
tical evolution equations.