  The main purpose of this paper is to apply the notion of hierarchical control
to a coupled degenerate non linear parabolic equations. We use the
Stackelberg-Nash strategy with one leader and two followers. The followers
solve a Nash equilibrium corresponding to a bi-objective optimal control
problem and the leader a null controllability problem. Since the considered
problem is non linear, the associated cost is non-convex. We first prove the
existence, uniqueness and the characterization of the Nash quasiequilibrium,
which is a weak formulation of the Nash equilibrium because the cost associated
to the non linear problem is non-convex. Next, we show that under suitable
conditions, the Nash quasi-equilibrium is equivalent to the Nash equilibrium.
Finally using some Carleman inequalities that we established, and the
Kakutani's fixed point Theorem, we brough the states of our system to the rest
at final time T .
