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Unlike convectional omnidirectional sensors that always have an omni-angle of sensing range, directional sensors may have a limited angle of sensing range due to the technical constraints or cost considerations. A directional sensor network consists of a number of directional sensors, which can switch to several directions to extend their sensing ability to cover all the targets in a given area. Power conservation is still an important issue in such directional sensor networks. In this paper, we address the multiple directional cover sets (MDCS) problem of organizing the directions of sensors into a group of non-disjoint cover sets to extend the network lifetime. One cover set in which the directions cover all the targets is activated at one time. We prove the MDCS to be NP-complete and propose several algorithms for the MDCS. Simulation results are presented to demonstrate the performance of these algorithms.