We analyse the predictions for the inclusive branching ratio for B --> X(s)
gamma in a class of string-inspired SUSY models with non-universal soft-bre
aking A-terms. These models are particularly interesting since the non-univ
ersality of the A-terms plays an important role in providing new significan
t contributions to CP violation effects in kaon physics while respecting th
e severe bounds on electric dipole moments. We show that b --> s gamma do n
ot severely constrain the non-universality of these models. In particular,
at low tan B (tan B similar or equal to 2), our predictions are close to th
e universal case. For large tan beta (tan beta greater than or similar to 1
5), the effect of non-universality is enhanced and stronger constraints hol
d. We find that the parameter regions which are important for generating si
zeable contribution to epsilon'/epsilon, of order 2 x 10(-3), are not exclu
ded. (C) 2001 Elsevier Science B.V. All rights reserved.