For decades, query processing over uncertain databases has received much attention from the database community due to the pervasive data uncertainty in many real-world applications such as location-based services (LBS), sensor networks, business planning, biological databases, and so on. In this paper, we will study a novel query type, namely range-constrained probabilistic mutual furthest neighbor query (PMFN), over uncertain databases. PMFN retrieves a set of object pairs, (o_i,o_j), within a given query range Q, such that uncertain objects oi and o_j are the furthest neighbors of each other with high probabilities. In order to efficiently tackle the PMFN problem, we propose effective pruning methods, range, convex hull, and hypersphere pruning, for filtering out uncertain objects that can never appear in the PMFN answer set. Then, we also design spatial and probabilistic pruning methods to rule out false alarms of PMFN candidate pairs. Finally, we utilize a variant of the R∗-tree to integrate our proposed pruning methods and efficiently process ad hoc PMFN queries. Extensive experiments show the efficiency and effectiveness of our pruning techniques and PMFN query processing algorithms over real and synthetic data sets.