AbstractThis paper addresses the problem of local state feedback stabilization of a class of nonlinear systems, which have planar centre manifold. A new technique for designing centre manifold has been developed. Using this approach, a sufficient condition for stabilization of a class of nonlinear system is obtained. The approach has been specified for two particular critical cases: ‘zero centre’ with zero eigenvalue of multiplicity 2 and ‘oscillatory centre’ with a pair of pure imaginary eigenvalues. The control law, which stabilizes the overall system, is also presented. Some examples are presented to indicate how the present theorem may be implemented. Copyright © 2003 John Wiley & Sons, Ltd.