Task allocation for wireless sensor networks with multiple concurrent applications (such as target tracking and event detection) requires sharing applications' tasks (such as sensing and computation) and available network resources. In this paper, we model the distributed task allocation problem for multiple concurrent applications by using a reverse combinatorial auction, in which the bidders (sensor nodes) are supposed to bid cost values (according to their available resources) for accomplishing the subset of the applications' tasks. Trust management schemes consist of a powerful tool for the detection of unexpected node behaviors (such as faulty or malicious). It is critical for participants (i.e., bidders and auctioneer) to estimate each other's trustworthiness before initiating the task allocation procedure. To address this issue, we introduce a real-time trust management module for our auction system that is able to validate the reliable bid value and determine faulty nodes and malicious entities. The main objective of our task allocation scheme is to maximize the network lifetime by sharing tasks and network resources within applications, while enhancing the overall application quality of service (e.g., deadline). We also propose a heuristic two-phase winner determination protocol to deal with the combinatorial reverse auction problem. Simulation results show that the proposed scheme offers the promising performance and efficiency. Copyright © 2012 John Wiley & Sons, Ltd.