Using sequential trend break and panel data models, we investigate the unit root hypothesis for the inflation rates of thirteen OECD countries. With individual country tests, we find evidence of stationarity in only four of the thirteen countries. The results are more striking with the panel data model. We can strongly reject the unit root hypothesis both for a panel of all thirteen countries and for a number of smaller panels consisting of as few as three countries. The non-rejection of the unit root hypothesis for inflation is very fragile to even a small amount of cross-section variation.