Abstract. Analyzing tracking data of various types of moving objects is an interesting research problem with numerous real-world applications. Several works have focused on continuously monitoring the nearest neighbors of a moving object, while others have proposed similarity measures for finding similar trajectories in databases containing historical tracking data. In this work, we introduce the problem of continuously monitoring nearest trajectories. In contrast to other similar approaches, we are interested in monitoring moving objects taking into account at each timestamp not only their current positions but their recent trajectory in a defined time window. We first describe a generic baseline algorithm for this problem, which applies for any aggregate function used to compute trajectory distances between objects, and without any restrictions on the movement of the objects. Using this as a framework, we continue to derive an optimized algorithm for the cases where the distance between two moving objects in a time window is determined by their maximum or minimum distance in all contained timestamps. Furthermore, we propose additional optimizations for the case that an upper bound on the velocities of the objects exists. Finally, we evaluate the efficiency of our proposed algorithms by conducting experiments on three real-world datasets.