We develop a comparative study using the TARCH and EGARCH non-linear econometric models. We use them to describe Mexican stock market returns. We model daily series of returns for 30 stocks and the Stock Market Index (IPC) for the period between December 7, 2005 and August 1, 2011. Most of the series show leverage effects. The results also suggest that the AR(1)-EGARCH(1,1) model describes properly the aggregated returns of the stock market (measured by the IPC). They also show that the AR(1)-TGARCH(1,1) and AR(1)-EGARCH(1,1) models fit 19 and 11 stock return series, respectively. Finally, the results show that the return mean (variance) has decreased (increased) since August 2007.