  We consider a class of cross diffusion systems with degenerate (or porous
media type) diffusion which is inspired by models in mathematical
biology/ecology with zero self diffusions. Known techniques for scalar
equations are no longer available here as maximum/comparison principles are
generally unavailable for systems. However, we will provide the existence of
weak solutions to the degenerate systems under mild integrability conditions of
strong solutions to nondegenerate systems and show that they converge to a weak
solution of the degerate system. These conditions will be verified for the
model introduced by Shigesada {\it et al.}. Uniqueness of limiting and
unbounded weak solutions will also be proved.
