The mechanisms of the energy degradation of leading particle, of the effect
ive dissociation of C (C) over bar pair (the precursor of physical J/psi) i
n the colour electric field of strings, and of the hadronic absorption (bot
h baryon and meson) are introduced into the proposed hadron and string casc
ade model, JPCIAE. That has been used to calculate the J/psi suppression fa
ctors in pA, AB (with light projectile), and Pb + Pb collisions at 200 A Ge
V/c energy. The theoretical results reproduce simultaneously both the corre
sponding NA38 and NA50 data fairly well, which arises the question of wheth
er there art J/psi anomalous suppressions in 158 A GeV/c Pb + Pb collisions
.