The paper discusses a simple univariate nonlinear parametric time-series model for unemployment rates, focusing on the asymmetry observed in many OECD unemployment series. The model is based on a standard logistic smooth transition autoregressive model for the first difference of unemployment, but it also includes a lagged level term. This model allows for asymmetric behavior by permitting “local” nonstationarity in a globally stable model. Linearity tests are performed for a number of quarterly, seasonally unadjusted, unemployment series from OECD countries, and linearity is rejected for a number of them. For a number of series, nonlinearity found by testing can be modeled satisfactorily by use of our smooth transition autoregressive model. The properties of the estimated models, including persistence of the shocks according to them, are illustrated in various ways and discussed. Possible existence of moving equilibria in series not showing asymmetry is investigated and modeled with another smooth transition autoregressive model.