A novel procedure to test for linearity and unit root in a nonlinear framework is proposed by introducing a new model–the MT-STAR model–which has similar properties of the ESTAR model but reduces the effects of the identification problem and can also account for asymmetry in the adjustment mechanism towards equilibrium. The asymptotic distribution of the proposed unit root test is non standard and is derived. The power of the test is evaluated through a simulation study and some empirical illustrations on real exchange rates show its accuracy.