  The long time behavior of a couple of interacting asymmetric exclusion
processes of opposite velocities is investigated in one space dimension. We do
not allow two particles at the same site, and a collision effect (exchange)
takes place when particles of opposite velocities meet at neighboring sites.
There are two conserved quantities, and the model admits hyperbolic (Euler)
scaling; the hydrodynamic limit results in the classical Leroux system of
conservation laws, \emph{even beyond the appearence of shocks}. Actually, we
prove convergence to the set of entropy solutions, the question of uniqueness
is left open. To control rapid oscillations of Lax entropies via logarithmic
Sobolev inequality estimates, the symmetric part of the process is speeded up
in a suitable way, thus a slowly vanishing viscosity is obtained at the
macroscopic level. Following earlier work of the first author the stochastic
version of Tartar--Murat theory of compensated compactness is extended to
two-component stochastic models.
