This paper revisits the dynamics of unemployment rate for 29 OECD countries over the period of 1980-2013. Numerous empirical studies of the dynamics of unemployment rate are carried out within a linear framework. However, unemployment rate can show nonlinear behaviour as a result of business cycles or some idiosyncratic factors specific to labour market (Cancelo, 2007). Thus, as a testing strategy we first perform Harvey et al. (2008) linearity unit root test and then apply the newly ESTAR nonlinear unit root test suggested by Kruse (2011). This test has higher power than conventional unit root tests when time series exhibits nonlinear behaviour. Our empirical findings provide significant evidence in favour of unemployment rate stationarity for 25 countries. For robustness purpose, we have also used panel unit root tests without and with structural breaks. The results show that unemployment hysteresis hypothesis is strongly rejected when taking into account the cross-sectional and structural break assumptions. Thus, unemployment rates are expected to return back to their natural levels without executing any costly macroeconomic labour market policies by the OECD's governments.