Abstract: A statistical methodology for detecting influential observations in long-memory models is proposed. The identification of these influential points is carried out by case-deletion techniques. In particular, a Kullback-Leibler divergence is considered to measure the effect of a subset of observations on predictors and smoothers. These techniques are illustrated with an analysis of the River Nile data where the proposed methods are compared to other well-known approaches such as the Cook and the Mahalanobis distances. (c) 2008 Elsevier B.V. All rights reserved.