This paper investigates the forecasting performance of three popular variants of the non-linear GARCH models, namely VS-GARCH, GJR-GARCH and Q-GARCH, with the symmetric GARCH(1,1) model as a benchmark. The application involves ten European stock price indexes. Forecasts produced by each non-linear GARCH model and each index are evaluated using a common set of classical criteria, as well as forecast combination techniques with constant and non-constant weights. With respect to the standard GARCH specification, the non-linear models generally lead to better forecasts in terms of both smaller forecast errors and lower biases. In-sample forecast combination regressions are better than those from single Mincer-Zarnowitz regressions. The out-of-sample performance of combining forecasts is less satisfactory, irrespective of the type of weights adopted.