  In this paper, we consider a class of nonlinear reaction-hyperbolic systems
with relaxation terms as models for axonal transport in neuroscience. We show
the Kruzkov entropy-satisfying BV-solutions of the systems converge towards the
solution of an equilibrium model at the rate of $O(\sqrt{\delta})$ in L1 norm
as the relaxation time $\delta$ tends to zero. But we don't make sure the rate
is optimal.
