In this paper, we consider robust M-estimation fo time series models with both symmetric and asymmetric forms of hetroscedasticity related to the GARCH and GJR models. The class of estimators includes least absolute deviation (LAD), Huber's, Cauchy and B-estimator as well as the well known quasi maximum likelihood estimator (QMLE). Extensive simulations are used to check the relative performance of these estimators in both models and the weighted resampling distribution of M-estimators. Our study indicate that there are estimators that can perform better than QMLE and even outperform robust estimator such as LAD when the error distribution is heavy-tailed. These estimators are also applied to real data sets.