A common observation among economists on many economic time-series, including major financial time-series, is the asymmetrical movement between the downward phase and the upward phase of their sample paths. Since this feature of time irreversibility cannot be described by the Gaussian ARMA, ARIMA or ARCH time-series models, we propose stationary and non-stationary simultaneous switching autoregressive (SSAR) models, which are nonlinear switching time-series models. We discuss some properties of these time-series models and the estimation method for their unknown parameters. The asymmetrical conditional heteroscedasticity can be easily incorporated into the SSAR models. We also report a simple empirical result on Nikkei 225 Spot and Futures indices by using a non-stationary SSAR model. JEL Classification Numbers: C22, C32.