This paper analyzes the dynamics of the US inflation series using two classes of models : structural changes models and Long memory processes. For the first class, we use the Markov Switching (MS-AR) model of Hamilton (1989) and the Structural Change (SCH-AR) model using the sequential method proposed by Bai and Perron (1998, 2003). For the second class, we use the ARFIMA process developed by Granger and Joyeux (1980). Moreover, we investigate whether the observed long memory behavior is a true behavior or a spurious behavior created by the presence of breaks in time series. Our empirical results provide evidence for changes in mean, breaks dates coincide exactly with some economic and financial events such Vietnam War and the two oil price shocks. Moreover, we show that the observed long memory behavior is spurious and is due to the presence of breaks in data set.