Asymmetric behavior has been documented in post-war quarterly U.S. unemployment rates. This suggests that improvement over conventional linear forecasts may be possible through use of nonlinear time series models. In this paper an out-of-sample forecasting competition is carried out for a set of leading nonlinear time series models. It is shown that several nonlinear forecasts do indeed dominate the linear forecast. The results are sensitive, however, to whether a stationarity-inducing transformation is applied to the nonstationary unemployment rate series.