This paper considers the application of long memory processes to describe in ‡ation with seasonal behaviour. We use three di¤erent long memory models taking into account the seasonal pattern in the data. Namely, the ARFIMA model with deterministic seasonality, the ARFISMA model, and the periodic ARFIMA (PARFIMA) model. These models are used to describe the in ‡ation rates of four di¤erent countries, USA, Canada, Tunisia, and South Africa. The analysis is carried out using the Sowell's (1992) maximum likelihood techniques for estimating ARFIMA model and using the approximate maximum likelihood method for the estimation of the PARFIMA process. We implement a new procedure to obtain the maximum likelihood estimates of the ARFISMA model, in which dummies variables on additive outliers are included. The advantage of this parametric estimation method is that all parameters are estimated simultaneously in the time domain. For all countries, we …nd that estimates of di¤erencing parameters are signi…cantly di¤erent from zero. This is evidence in favour of long memory and suggests that persistence is a common feature for in ‡ation series. Note that neglecting the existence of additive outliers may possibly biased estimates of the seasonal and periodic long memory models.