Anomaly detection has received considerable interest for hyperspectral data exploitation due to its high spectral resolution. A well-known algorithm for hyperspectral anomaly detection is the RX detector. A number of variations have been studied since then, including global and local versions for different type of anomalies. Aiming at a real-time requirement for practical applications, this paper extends the concept of global and local anomaly detectors to be real-time detectors. The algorithms exploit the fact that a true real-time detector must produce its output in a causal manner and at the same time as an input comes in. Taking advantage of the Woodbury matrix identity, the global and local real-time detectors can be implemented and processed pixel-by-pixel in real time. Both synthetic and real hyperspectral imagery are conducted to demonstrate their performance.