In this study we employ augmented and switching time series models to find possible existence of business cycle asymmetries in U.S. stock returns. Our approach is fully parametric and testing strategy is robust to any conditional heteroskedasticity, and outliers that may be present. We also approximate in sample as well as out-of-sample forecasts from artificial neural networks for testing business cycle nonlinearities in U.S. stock returns. Our results based on nonlinear augmented and switching time series models show a strong evidence of business cycle asymmetries in conditional mean dynamics of U.S. stock returns. These results also show that conditional heteroskedasticity is unimportant when testing for asymmetries in conditional mean. Moreover, the conditional volatility in stock returns is asymmetric and is more pronounced in recessions than in expansion phase of business cycles. Similarly, the results based on neural network models show a statistically significant evidence of business cycle nonlinearities in US stock returns. The magnitude of these nonlinearities is more obvious in post World War II era than in the full sample period.