This paper analyses the degree of inflation persistence in the EU15, the euro area and each of its member states using disaggregate price indices from the Harmonised Index of Consumer Prices. Our results reveal substantial heterogeneity across countries and indices. The overall results, based on both parametric and non-parametric persistence measures, suggest a very moderate degree of median and mean inflation persistence. For most price indices we are able to reject the unit root hypothesis, as well as the notion of disaggregate inflation exhibiting a high degree of persistence. Durable goods and services tend to be relatively less persistent than other indices. Aggregation effects, both across indices and countries, tend to be present. We find structural breaks both owing to the change in the monetary regime and to the modified treatment of sales in the official HICP series. The latter tends to reduce the measured degree of inflation persistence.