This paper is concerned with nonlinear transfer function analysis. We propose a test statistic to detect nonlinearity of a transfer function. Simulation study shows that the test works reasonably well in finite samples for the nonlinear models commonly used in the literature. We then discuss nonlinear transfer function modeling and the contribution of nonlinear components in a given model. For illustration, we apply the test to several data sets and use a real example to show that Substantial gain may result from using simple nonlinear transfer Functions.