This article estimates generalized ARCH (GARCH) models for German stock market indices returns, using weekly and monthly data, various GARCH specifications and (non)normal error densities, and a variety of diagnostic checks. German stock return series exhibit significant levels of second-order dependence. Our results clearly demonstrate that for both weekly as well as monthly return series the Student-t distribution is superior to the standard normal distribution. In particular, the estimated GARCH-t models appear to be reasonably successful in accounting for both observed leptokurtosis and conditional heteroskedasticity from German stock return movements.