The paper appraises the in-sample and out-of-sample adequacy of linear AR and nonlinear SETAR models of unemployment rates for Germany, Japan, the UK and the US. Tests are reported for the presence and specification of threshold nonlinearities, SETAR model estimates, limiting dynamic properties and residual diagnostics, and out-of-sample forecasting performance. In-sample, threshold non-linearities are confirmed to be strongly present for the UK, US and Germany, and more marginally so for Japan. Out-of-sample, excepting Japan, SETAR models provide superior onestep-ahead forecast on RMSE grounds, most notably for the US. Final tests indicate that these models exhibit predictive accuracy in the sense of parameter and residual variance stability, implying the potential for exploitation of such nonlinearity in official forecasting.