Numerous applications require continuous publication of statistics for monitoring purposes, such as real-time traffic analysis, timely disease outbreak discovery, and social trends observation. These statistics may be derived from sensitive user data and, hence, neces- sitate privacy preservation. A notable paradigm for offering strong privacy guarantees in statistics publishing is ε-differential privacy. However, there is limited literature that adapts this concept to set- tings where the statistics are computed over an infinite stream of "events" (i.e., data items generated by the users), and published periodically. These works aim at hiding a single event over the en- tire stream. We argue that, in most practical scenarios, sensitive information is revealed from multiple events occurring at contigu- ous time instances. Towards this end, we put forth the novel notion of w-event privacy over infinite streams, which protects any event sequence occurring in w successive time instants. We first formu- late our privacy concept, motivate its importance, and introduce a methodology for achieving it. We next design two instantiations, whose utility is independent of the stream length. Finally, we con- firm the practicality of our solutions experimenting with real data.