  We prove global existence in time of solutions to relaxed conservative cross
diffusion systems governed by nonlinear operators of the form $u_i\to
\partial_tu_i-\Delta(a_i(\tilde{u})u_i)$ where the $u_i, i=1,...,I$ represent
$I$ density-functions, $\tilde{u}$ is a spatially regularized form of
$(u_1,...,u_I)$ and the nonlinearities $a_i$ are merely assumed to be
continuous and bounded from below. Existence of global weak solutions is
obtained in any space dimension. Solutions are proved to be regular and unique
when the $a_i$ are locally Lipschitz continuous.
