We examine the unemployment hysteresis hypothesis for 31 European countries, the USA and Japan, using alternative linear and nonlinear unit root tests, taking into account possible structural breaks. Two types of smooth transition models—Exponential Smooth Transition Autoregressive and Asymmetric Exponential Smooth Transition Autoregressive—are employed to account for the nonlinear mean-reverting behaviour in unemployment due to heterogeneity in hiring and firing costs across firms. Four main results emerge: first, the hysteresis hypothesis is rejected for 60 % of the countries in our sample. Second, nonlinear models capture the asymmetries in unemployment dynamics over the business cycle for some countries. Third, many of the series display multiple structural breaks which might point out shifts in mean level of unemployment. Fourth, forecasting powers of our nonlinear models display poor performance against the linear AR specification. The results have policy implications for the debate on the benefits of demand or supply-side policies for tackling the current unemployment problem in Europe.