Effects of aftershocks were thoroughly discussed by the first author with an extensive review of existing publications and research regarding this topic (Touileb 2013). Although not taken into account on a systematic basis, in dam design and safety, recently recorded aftershocks are found increasingly stronger than usually assumed. The other aspect that should be considered is the response of a given large dam that is expected to be strongly shaken several times during its very long service life. Such an issue is obviously more relevant in the case of high seismic hazard areas. For instance, the formation of plastic shear bands in the shoulders of the dam due to an experienced strong earthquake motions, that is confirmed by physical observation of permanent deformation and cracks such as at the crest of the dam, modifies completely the dam initial conditions before the next strong earthquakes. Dynamic non-linear analysis of large rockfill and earthfill dams under the transient loading of a strong earthquake motion leads usually to the manifestation of strong non-linearities, together with the creation of final conditions that are, in general, different from the initial conditions. Such an aspect is not taken into account on a regular basis. However, it is believed that it requires some attention in order to reduce the risks associated to the seismic hazard under all its types of manifestation.