The ability to timely process significant amounts of continuously updated spatial data is mandatory for an increasing number of applications. Parallelism enables such applications to face this data-intensive challenge and allows the devised systems to feature low latency and high scalability. In this paper, we focus on a specific data-intensive problem concerning the repeated processing of huge amounts of range queries over massive sets of moving objects, where the spatial extent of queries and objects is continuously modified over time. To tackle this problem and significantly accelerate query processing, we devise a hybrid CPU/GPU pipeline that compresses data output and saves query processing work. The devised system relies on an ad-hoc spatial index leading to a problem decomposition that results in a set of independent data-parallel tasks. The index is based on a point-region quadtree space decomposition and allows to tackle effectively a broad range of spatial object distributions, even those very skewed. Also, to deal with the architectural peculiarities and limitations of the GPUs, we adopt non-trivial GPU data structures that avoid the need of locked memory accesses while favouring coalesced memory accesses, thus enhancing the overall memory throughput. To the best of our knowledge, this is the first work that exploits GPUs to efficiently solve repeated range queries over massive sets of continuously moving objects, possibly characterized by highly skewed spatial distributions. In comparison with state-of-the-art CPU-based implementations, our method highlights significant speedups in the order of 10 - 20x, depending on the dataset. Copyright (C) 2016 John Wiley & Sons, Ltd.