We systematically examine the comparative predictive performance of a number of alternative non-linear models for stock and bond returns in the G7 countries. Besides, Markov switching, threshold, and smooth transition regime switching (predictive) regression models, we also estimate univariate models in which conditional heteroskedasticity is captured through TARCH, GARCH and EGARCH models and ARCH-in mean effects appear in the conditional mean. Although we fail to find a consistent winner/out-performer across all countries and asset markets, it turns out that capturing non-linear effects is of extreme importance to improve forecasting performance. U.S. and U.K. asset return data are “special ” in the sense that good predictive performance seems to loudly ask for non-linear effects, especially of the Markov switching type. Although occasionally also stock and bond returns from other G7 countries appear to require non-linear modeling (especially of TAR and STAR type), data from France, Germany, and Italy express interesting predictive results on the basis of simpler benchmarks. U.S. and U.K. data are also the only two data sets in which we find statistically significant differences between forecasting models.