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Caching valid regions of spatial queries at mobile clients is effective in reducing the number of queries submitted by mobile clients and query load on the server. However, mobile clients suffer from longer waiting time for the server to compute valid regions. We propose in this paper a proxy-based approach to continuous nearest-neighbor (NN) and window queries. The proxy creates estimated valid regions (EVRs) for mobile clients by exploiting spatial and temporal locality of spatial queries. For NN queries, we devise two new algorithms to accelerate EVR growth, leading the proxy to build effective EVRs even when the cache size is small. On the other hand, we propose to represent the EVRs of window queries in the form of vectors, called estimated window vectors (EWVs), to achieve larger estimated valid regions. This novel representation and the associated creation algorithm result in more effective EVRs of window queries. In addition, due to the distinct characteristics, we use separate index structures, namely EVR-tree and grid index, for NN queries and window queries, respectively. To further increase efficiency, we develop algorithms to exploit the results of NN queries to aid grid index growth, benefiting EWV creation of window queries. Similarly, the grid index is utilized to support NN query answering and EVR updating. We conduct several experiments for performance evaluation. The experimental results show that the proposed approach significantly outperforms the existing proxy-based approaches.