We test the hypothesis that the long-term Phillips curve is downward sloping and has become flatter in the last 10 to 15 years. Controlling for the most important other factors influencing the inflation rate, we estimate cointegrations and test whether a »break« in the Phillips curve can be detected. We restrict our study to Germany, France, Italy, Spain, the UK and the USA. The results vary considerably between the countries, but all exhibit a downward sloping long-run Phillips curve and show the presumed »break«. First we explain the results by changes in the wage or price setting circumstance. Then we critically discuss explanations based on the time-varying NAIRU and put against them explanations based on aggregate demand and hysteresis. In the conclusion, some consequences for economic policy are indicated.