Attempts by governments to finance a substantial proportion of expenditure by seigniorage can lead to multiple inflationary equilibria. Theoretical models suggest that, in these circumstances, inflation follows a non-linear process with up to three steady states and that the stability characteristics of these depend on the process by which expectations are formed. In this paper we show that the exponential smooth transition autoregression (ESTAR) model is capable of exhibiting the required characteristics and so provides a suitable vehicle for analysing inflation in high inflation economies. We estimate ESTAR models for three well-known inflationary episodes—the German hyperinflation of the early 1920s and post-Second World War inflations in Argentina and Brazil. Our results imply that, during the periods in question, each of these economies possessed a stable low-level equilibrium rate of inflation but that the variances of inflation shocks were large enough to drive each economy into a high inflation state. For Brazil, this high inflation state is stable around a particular value but in the cases of Argentina and Germany the high inflation state is characterized by inflation cycles.