  We investigate the evolution of the mass function of the Galactic globular
cluster system (GCMF) taking into account the effects of stellar evolution,
two-body relaxation, disk shocking and dynamical friction on the evolution of
individual globular clusters.We have adopted a log-normal initial GCMF and we
have studied in detail the dependence on the initial dispersion and mean value
of the GCMF of the fraction of the initial number of clusters surviving after
one Hubble time, of the final GCMF, and of the difference between the
properties of the GCMF of clusters closer to the Galactic center and of those
in the outer regions of the Galaxy.The initial log-normal shape of the GCMF is
preserved in most cases and if a power-law in M is adopted for the initial
GCMF, evolutionary processes tend to modify it into a log-normal GCMF. The
difference between initial and final values of dispersion and mean value of the
GCMF as well as the difference between the final values of these parameters for
inner and outer clusters can be positive or negative depending on initial
conditions.A significant effect of evolutionary processes does not necessarily
give rise to a strong trend of the mean value of the GCMF with the
galactocentric distance.The existence of a particular initial GCMF able to keep
its initial shape and parameters unaltered during the entire evolution through
a subtle balance between disruption of clusters and evolution of the masses of
those which survive,suggested in Vesperini(1997),is confirmed. (abridged)
