The aim of this paper is to provide qualitative models characterizing interdependencies related failures of two critical infrastructures: the electricity infrastructure and the associated information infrastructure. The interdependencies of these two infrastructures are increasing due to a growing connection of the power grid networks to the global information infrastructure, as a consequence of market deregulation and opening. These interdependencies increase the risk of failures. We focus on cascading, escalating and common-cause failures, which correspond to the main causes of failures due to interdependencies. We address failures in the electricity infrastructure, in combination with accidental failures in the information infrastructure, then we show briefly how malicious attacks in the information infrastructure can be addressed.