We study large time behaviour of viscous perturbations of the Keyfitz-
Kranzer system. We restrict our attention to isotropic solutions. Para
bolic perturbations which enable the propagation of such solutions are
computed. We describe the behaviour of their solutions for large time
. Numerical perturbations are also studied, in the particular case of
the Godunov scheme. We prove the existence of an explicit parabolic pe
rturbation, whose dynamics for large time coincides with the Godunov s
cheme's one.