This paper investigates inequality persistence in a group of 21 OECD countries using linear and non-linear fractionally integrated methods. Using linear models, the results show that the series are strongly persistent which implies lack of average reversal and permanency of shocks. Mean reversion is only found in the case of Finland and partial evidence of mean reversion is detected for Belgium, Greece, Austria and the Netherlands. The results are similar using non-linear methods. Mean reversion is only found in the case of Finland, Belgium, Greece and Spain. Although, most countries show no evidence of non-linear structures except for four countries, namely, Finland, Spain, the United Kingdom and the United States. The implications of the empirical findings are reported at the end of the manuscript. [ABSTRACT FROM AUTHOR]