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One of the major applications of wireless ad hoc networks is to extend the Internet coverage and support pervasive and efficient data dissemination and sharing. To reduce data access cost and delay, caching has been widely used as an important technique. The efficiency of data access in caching systems largely depends on the cost for maintaining cache consistency, which can be high in wireless ad hoc networks due to network dynamism. Therefore, to make better trade-off between cache consistency and the cost incurred, it would be highly desirable to provide users the flexibility in specifying consistency requirements for their applications. In this paper, we propose a general consistency model called Probabilistic Delta Consistency (PDC), which integrates the flexibility granted by existing consistency models, covering them as special cases. We also propose the Flexible Combination of Push and Pull (FCPP) algorithm which satisfies user-specified consistency requirements under the PDC model. The analytical model of FCPP is used to derive the balance of minimizing the consistency maintenance cost and ensuring the specified consistency requirement. Extensive simulations are conducted to evaluate whether FCPP can satisfy arbitrarily specified consistency requirements, and whether FCPP works cost-effectively in dynamic wireless ad hoc networks. The evaluation results show that FCPP can adaptively tune itself to satisfy various user-specified consistency requirements. Moreover, it can save the traffic cost by up to 50 percent and reduce the query delay by up to 40 percent, compared with the widely used Pull with TTR algorithm.