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This paper describes a new robust appearance-based method for representing and recognizing human behaviours using the eigenspace technique. This method has three main advantages over the existing appearance-based methods. First, the centering of the human-body blob, in each background-subtracted video frame, together with the use of an incremental procedure for compression, have made the extraction of the motion features limited to the smallest possible area in the image. Second, a learning strategy based on the eigen-space technique is employed for dimensionality reduction using the Linear Discriminant Analysis algorithm (LDA), while providing maximum separability between classes. Third, data retrieving has been greatly enhanced by using a directed acyclic graph (DAG) structure based on the Euclidean distance between projected data. The system has been tested using a large number of training motion videos partitioned into 6 human behaviours (boxing, hand-clapping, hand-waving, jogging, running, and walking) captured for 25 different persons in 2 different scenarios (indoor and outdoor). The experimental results are very good, showing a high performance level of the proposed method.