The ability to timely process significant amounts of continuously updated spatial data is mandatory for an increasing number of applications. In this paper we focus on a specific data-intensive problem concerning the repeated processing of huge amounts of k nearest neighbours (k-NN) queries over massive sets of moving objects, where the spatial extents of queries and the position of objects are continuously modified over time. In particular, we propose a novel hybrid CPU/GPU pipeline that significantly accelerate query processing thanks to a combination of ad-hoc data structures and non-trivial memory access patterns. To the best of our knowledge this is the first work that exploits GPUs to efficiently solve repeated k-NN queries over massive sets of continuously moving objects, even characterized by highly skewed spatial distributions. In comparison with state-of-the-art sequential CPU-based implementations, our method highlights significant speedups in the order of 10x-20x, depending on the datasets, even when considering cheap GPUs.