This paper investigates the potential nonlinear relationship between the real exchange rates of two currencies (Chinese Yuan and South Korean Won) and economic fundamentals using quarterly data over the period 1980Q1-2009Q4. We employ the Alternating Conditional Expectation algorithm to test for nonlinearity among the variables of interest. The results show that there does exist a nonlinear cointegrating relationship between the real exchange rates and fundamentals for China and Korea. In contrast with the conventional linear relationship, the elasticity of the real exchange rate with respect to fundamentals varies over time according to the nonlinear relationship.