This paper empirically investigates the possibility of self-sustained oscillations at business cycle frequency. The theoretical model considers aggregate economic activity and the functional income distribution in the spirit of Goodwin (1967). In the empirical investigation, we utilize four measures each of economic activity and the labor share for the US post-war macroeconomy. Using Schuster’s periodogram, we first show that these time series have an important frequency peak at about forty quarters. We therefore detrend them with wavelet methods. To allow for nonlinear dynamic interaction, we introduce a feedforward neural network (FNN). This method is first shown to correctly identify stability or a limit cycle in simulations of the theoretical model with reasonable noise and sample size. Estimation results provide some support for a limit cycle in the post-war US, but this evidence is not independent of detrending methods used.