This paper describes a self-stabilizing version of an algorithm presented by A. Mazurkiewicz [Inform. Process. Lett. 61 (1997) 233–239] for enumerating nodes by local rules on an anonymous network. The result improves the reliability aspects of the original algorithm and underlines the importance of a non-ambiguous topology for a network. 2001 Elsevier Science B.V. All rights reserved.