Due to advances of hyperspectral imaging sensors many unknown and subtle targets that cannot be resolved by multispectral imagery can now be uncovered by hyperspectral imagery. These targets generally cannot be identified by visual inspection or prior knowledge, but yet provide crucial and vital information for data exploitation. One such type of targets is anomalies which have recently received considerable interest in hyperspectral image analysis. Many anomaly detectors have been developed and most of them are based on the most widely used Reed-Yu's algorithm, called RX detector (RXD). However, a key issue in making RX detector-like anomaly detectors effective is how to effectively utilize the spectral information provided by data samples, e.g., sample covariance matrix used by RXD. Recently, a dual window-based eigen separation transform (DWEST) was developed to address this issue. This paper extends the concept of DWEST to develop a new approach, to be called multiple-window anomaly detection (MWAD) by making use of multiple windows to perform anomaly detection adaptively. As a result, MWAD is able to detect anomalies of various sizes using multiple windows so that local spectral variations can be characterized and extracted by different window sizes. By virtue of this newly developed MWAD, many existing RXD-like anomaly detectors including DWEST can be derived as special cases of MWAD.