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Person Re-Identification (ReID) is a challenging problem in many video analytics and surveillance applications, where a person's identity must be associated across a distributed non-overlapping network of cameras. Video-based person ReID has recently gained much interest because it allows capturing discriminant spatio-temporal information from video clips that is unavailable for image-based ReID. Despite recent advances, deep learning (DL) models for video ReID often fail to leverage this information to improve the robustness of feature representations. In this paper, the motion pattern of a person is explored as an additional cue for ReID. In particular, a flow-guided Mutual Attention network is proposed for fusion of image and optical flow sequences using any 2D-CNN backbone, allowing to encode temporal information along with spatial appearance information. Our Mutual Attention network relies on the joint spatial attention between image and optical flow features maps to activate a common set of salient features across them. In addition to flow-guided attention, we introduce a method to aggregate features from longer input streams for better video sequence-level representation. Our extensive experiments on three challenging video ReID datasets indicate that using the proposed Mutual Attention network allows to improve recognition accuracy considerably with respect to conventional gated-attention networks, and state-of-the-art methods for video-based person ReID.