Abstract Stream reasoning is the task of continuously deriving conclusions on streaming data. To get results instantly one evaluates a query repeatedly on recent data chunks selected by window operators. However, simply recomputing results from scratch is impractical for rule-based reasoning with semantics similar to Answer Set Programming, due to the trade-off between complexity and data throughput. To address this problem, we present a method to efficiently update models of a rule set. In particular, we show how an answer stream (model) of a LARS program can be incrementally adjusted to new or outdated input by extending truth maintenance techniques. We obtain in this way a means towards practical rule-based stream reasoning with nonmonotonic negation, various window operators and different forms of temporal reference.