AbstractThis paper gives fast O(n2) algorithms for the factorization of positive‐definite and indefinite Hankel matrices. The algorithms are based on the concept of displacement structure and are valid for the more general class of Hankel‐like matrices. The positive‐definite algorithm is proven to be backward stable. The indefinite algorithm uses a look‐ahead step that is naturally suggested by displacement approach. Our error analysis suggests a new criterion for the size of the look‐ahead step and our numerical experiments suggest that the use of the new criterion allows us to ensure numerical stability in practice. Copyright © 2001 John Wiley & Sons, Ltd.