This article develops the dynamic asymmetric GARCH (or DAGARCH) model that generalizes asymmetric GARCH models such as that of Glosten, Jagannathan, and Runkle (GJR), introduces multiple thresholds, and makes the asymmetric effect time dependent. We provide the stationarity conditions for the DAGARCH model and show how GJR can be obtained as a special case. Furthermore, we derive the news impact curve implied by the DAGARCH model and demonstrate its flexibility. An application to daily stock market indices is presented to demonstrate the practical usefulness of the new model.