  We study general zero range processes with different types of particles on a
d-dimensional lattice with periodic boundary conditions. A necessary and
sufficient condition on the jump rates for the existence of stationary product
measures is established. For translation invariant jump rates we prove the
hydrodynamic limit on the Euler scale using Yau's relative entropy method. The
limit equation is a system of conservation laws, which are hyperbolic and have
a globally convex entropy. We analyze this system in terms of entropy
variables. In addition we obtain stationary density profiles for open
boundaries.
