Abstract: Zero dynamics algorithm for general nolinear control systems is proposed, in which we need only very mild ragularity assumptions, namly, the constancy of the dimensions of certain distributions (and/or of the ranks of certain mappings) around a given point. From the zero dynamics algorithm the norm form for general nolinear control systems is presented, which is extension of the affine nonlinear systems. Last, we study one of the applications of the norm form to the problem of local feedback asymptotic stabilization. This result does not require asymptotic stability in the first approximation for the zero dynamics, so that it may be useful in order to solve critical problems of local feedback asymptotic stabilization.