This paper proposes a new testing strategy for unemployment hysteresis as the joint restriction of a unit-root in the unemployment rate and no feedback effect of unemployment in the Phillips wage equation. The associated test statistics are derived when this joint restriction is imposed and when a sequential two steps testing strategy is adopted. An empirical application leads to reject the null hypothesis of wage hysteresis for most of our OECD countries. Evidence against hysteresis is reinforced when accounting for wage adjustments in the bivariate approach. Copyright Springer-Verlag Berlin Heidelberg 2003Key words: hysteresis, unemployment persistence, unit root, wage adjustments, Wald tests., JEL classification: C12, C22,