  We consider one-dimensional, locally finite interacting particle systems with
two conservation laws. The models have a family of stationary measures with
product structure and we assume the existence of a uniform bound on the inverse
of the spectral gap which is quadratic in the size of the system. Under
Eulerian scaling the hydrodynamic limit for the macroscopic density profiles
leads to a two-component system of conservation laws. The resulting pde is
hyperbolic inside the physical domain of the macroscopic densities, with
possible loss of hyperbolicity at the boundary. We investigate the propagation
of small perturbations around a \emph{hyperbolic} equilibrium point. We prove
that the perturbations essentially evolve according to two \emph{decoupled}
Burgers equations. The scaling is not Eulerian: if the lattice constant is
$n^{-1}$, the perturbations are of order $n^{-\beta}$ then time is speeded up
by $n^{1+\b}$. Our derivation holds for $0<\beta< \frac15$. The proof relies on
Yau's relative entropy method, thus it applies only in the regime of smooth
solutions.
