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This paper addresses the problem of exploiting spatiotemporal information to improve small object detection precision in video. We propose a two-stage object detector called FANet based on short-term spatiotemporal feature aggregation and long-term object linking to refine object detections. First, we generate a set of short tubelet proposals. Then, we aggregate RoI pooled deep features throughout the tubelet using a new temporal pooling operator that summarizes the information with a fixed output size independent of the tubelet length. In addition, we define a double head implementation that we feed with spatiotemporal information for spatiotemporal classification and with spatial information for object localization and spatial classification. Finally, a long-term linking method builds long tubes with the previously calculated short tubelets to overcome detection errors. The association strategy addresses the generally low overlap between instances of small objects in consecutive frames by reducing the influence of the overlap in the final linking score. We evaluated our model in three different datasets with small objects, outperforming previous state-of-the-art spatiotemporal object detectors and our spatial baseline.