  For a class of reaction cross-diffusion systems of two equations with a
cross-diffusion term in the first equation and with self-diffusion terms, we
prove that the unique local smooth solution given by Amann theorem is actually
global. This class of systems arises in Population dynamics, and extends the
triangular Shigesada-Kawasaki-Teramoto system when general power-laws growth
are considered in the reaction and diffusion rates.
