Moving queries over mobile objects are an important type of query in moving object database systems. In recent years, there have been quite a few works in this area. Due to the high frequency in location updates and the expensive cost of continuous query processing, server computation capacity and wireless communication bandwidth are the two limiting factors for large-scale deployment of moving object database systems. Many techniques have been proposed to address the server bottleneck including one using distributed servers. To address both scalability factors, distributed query processing techniques have been considered. These schemes enable moving objects to participate in query processing to substantially reduce the demand on server computation, and wireless communications associated with location updates. Most of these techniques, however, assume an open-space environment. Since Euclidean distance is different from network distance, techniques designed specifically for an open space cannot be easily adapted for a spatial network. In this paper, we present a distributed framework which can answer moving query over moving objects in a spatial network. To illustrate the effectiveness of the proposed framework, we study two representative moving queries, namely, moving range queries and moving k-nearest-neighbor queries. Detailed algorithms and communication mechanisms are presented. The simulation studies indicate that the proposed technique can significantly reduce server workload and wireless communication cost.