This dissertation focuses on testing for nonlinearities in time series. Inspired by the work of Luukkonen et al. (1988) and Saikkonen and Luukkonen (1988), we consider applying a linearity test constructed specifically to general linearity testing by utilizing the power of a specific linearity test against "incorrect" nonlinear models. The LM test is discussed as a specific linearity test. To evaluate its performance as a general linearity test, we introduce a popular general linearity test, the BDS test, for comparison. Both power and size properties of the tests are investigated using Monte Carlo simulation and Bootstrap methods. The data generating process are the linear AR model and the nonlinear BL, EAR, TAR, STAR and ARCH models. Though the powers of the LM tests vary according to the data generating process, as Luukkonen et al. (1988) and Saikkonen and Luukkonen (1988) concluded, we are able to find that the START, the LM test with the STAR model as alternative, has generally good powers for all the nonlinear models discussed. We apply the result to an empirical study of four major countries' foreign exchange rate series. Linearity tests in the form of START and BDS are conducted for the data. The START statistics indicate that all the four exchange rates series are nonlinear, while the BDS statistics only detect nonlinearities in three of the four series. We estimate the series in the nonlinear form of ESTAR and BL models. All of them are significant and most of them are better than the linear AR estimation. Meese and Rogoff's myth that nonlinear models cannot do better than the naive random walk model is also discussed for this specific data.