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The search for train connections in state-of-the-art commercial timetable information systems is based on a static schedule. Unfortunately, public transportation systems suffer from delays for various reasons. Thus, dynamic changes of the planned schedule have to be taken into account. A system that has access to delay information of trains (and uses this information within search queries) can provide valid alternatives in case a train change breaks. Additionally, it can be used to actively guide passengers as these alternatives may be presented before the passenger is already stranded at a station due to a broken transfer. In this work we present an approach which takes a stream of delay information and schedule changes on short notice (partial train cancellations, extra trains) into account. Primary delays of trains may cause a cascade of so-called secondary delays of other trains which have to wait according to certain waiting policies between connecting trains. We introduce the concept of a dependency graph to efficiently calculate and update all primary and secondary delays. This delay information is then incorporated into a time-expanded search graph which has to be updated dynamically. These update operations are quite complex, but turn out to be not time-critical in a fully realistic scenario. We finally present a case study with data provided by Deutsche Bahn AG showing that this approach has been successfully integrated into our multi-criteria timetable information system MOTIS and can handle massive delay data streams instantly.