In this paper we introduce and test the hypothesis that the relation between inflation and unemployment has been in many countries subject to a significant change in the early 1990's after the disinflation period. That period began between 1975 and 1980 after the first (or the second) oil price shock in autumn 1973. During the disinflation period, inflation and unemployment were the result of the struggle between the wage and price setters trying to influence the distribution of income to their favour and the Central Bank fighting against inflation. Since the wage and price setters did not fully believe in an "unconditional" pursuit of the anti-inflationary policy, the result was a gradual decline of the inflation rate rendered possible by a rising rate of unemployment. Our hypothesis was inspired by the observation that the statistical Phillips curves are now rather flat in many countries. If such horizontal Phillips curves will also result when they are estimated taking into account the most important other factors influencing the inflation rate (mainly supply shocks) they may be explained by the hypothesis that during the 1990's, wage and price setters finally accepted the new rigour of the monetary policy and tried no more (nor had the market power { due to increasing globalisation and international competition) to pursue a policy which raises the inflation rate significantly above the target inflation rate of the Central Bank. In that case a "break" in the parameters of the Phillips- Curve should be observed. We use econometric methods to test whether the presumed \break" in the relation between inflation and unemployment can be shown to exist. We restrict our study to the four largest countries of the Euro area (Germany, France, Italy and Spain), the UK and the USA. The result are very different for the countries; therefore we intend in a further step to detect the reasons for there divergences.