In this paper we test the inflation persistence hypothesis as well as model the long run behaviour of inflation rates in a pool of African countries, using a non-linear framework. In order to do so, we rely on unit root tests applied to non-linear models and fractional integration. The result shows that the hypothesis of inflation persistance does not hold empirically for most of the countries. In addition, the estimated models (logistic smooth transition autoregression, LSTAR) are stable, in the sense that the variable tends to remain in the regime (low inflation or high inflation) once reached and changes between regimes are only achieved after a shock. The results also indicate that the effects of the shocks on inflation tend to die out; exogenous factors, i.e. supply shocks and inertia may be causing this outcome, as they play a substantial role in the determination of the inflation rates for our selected African countries.