We study the exponential stabilization problem for a
nonlinear Korteweg-de Vries equation on bounded interval in cases where
the linearized control system is not controllable. The system has
Dirichlet boundary conditions at the end-points of the interval, a
Neumann nonhomogeneous boundary condition at the right end-point which
is the control. We build a class of time-varying feedback laws
for which the solutions of the closed-loop systems with small
initial data decay exponentially to 0. We present also results on the
well-posedness of the closed-loop systems for general time-varying
feedback laws.