We propose a term structure model featuring double-autoregressive dynamics, which can accommodate unit roots and cointegrating relations while maintaining stationarity. In an empirical application, the model reduces in-sample misspecification and significantly improves out-of-sample yield forecasts compared with term structure models based on linear VAR dynamics. The double-autoregressive process implies term premia that resemble the term spread. We test whether these premia help in overcoming the persistence problem of stationary VAR models with mixed results. Finally, we discuss alternative interpretations of the mechanism inducing stationarity in our model.