  In this paper, we are concerned with the internal control of a class of
one-dimensional nonlinear parabolic systems with nonlocal and weakly degenerate
diffusion coefficients. Our main theorem establishes a local null
controllability result with only one internal control for a system of two
equations. The proof, based on the ideias developed by Fursikov and Imanivilov,
is obtained from the global null controllability of the linearized system
provided by \textit{Lyusternik's Inverse Mapping Theorem}. This work extends
the results previously treated by the authors for just one equation. For the
system, the main issue is to obtain similar results with just one internal
control, which requires a new Carleman estimate with the local term just
depending on one of the state function.
