We present a system for online, incremental composite event recognition. In streaming environments, the usual case is for data to arrive with a (variable) delay from, and to be revised by, the underlying sources. We propose RTECinc, an incremental version of RTEC, a composite event recognition engine with formal, declarative semantics, that has been shown to scale to several real-world data streams. RTEC deals with delayed arrival and revision of events by computing all queries from scratch. This is often inefficient since it results in redundant computations. Instead, RTECinc deals with delays and revisions in a more efficient way, by updating only the affected queries. We examine RTECinc theoretically, presenting a complexity analysis, and show the conditions in which it outperforms RTEC. Moreover, we compare RTECinc and RTEC experimentally using real-world and synthetic datasets. The results are compatible with our theoretical analysis and show that RTECinc outperforms RTEC in many practical cases.