  In the present work, we consider nonlinear control systems for which there
exist structural obstacles to the design of classical continuous backstepping
feedback laws. We conceive feedback laws such that the origin of the
closed-loop system is not globally asymptotically stable but a suitable
attractor (strictly containing the origin) is practically asymptotically
stable. A design method is suggested to build a hybrid feedback law combining a
backstepping controller with a locally stabilizing controller. A constructive
approach is also suggested employing a differential inclusion representation of
the nonlinear dynamics. The results are illustrated for a nonlinear system
which, due to its structure, does not have {\it a priori} any globally
stabilizing backstepping controller.
