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In this paper, we propose a new framework for distributed speech processing over wireless mesh networks (WMNs). State of the art distributed speech processing systems address issues of sending information over centralized networks namely, cellular networks and wireless LANs whose main functionality is to switch and route packets from one location to another. Here we propose a method for distributed speech processing over WMNs, which are inherently fault tolerant and simpler to set up in many civilian and tactical applications. We also address issues of multi stream speech processing over WMNs both in terms of computational complexity and time using two standard routing protocols namely the dynamic source routing and the Bellman Ford protocols at different packet losses. As a proof of concept we illustrate the results of distributed speaker recognition over a thirty node WMN with ten speakers simultaneously accessing the network in various packet loss scenarios. The advantages and issues in implementing distributed speech processing systems over WMNs are also discussed. Analytical estimates show that on an average, for a 20 hop path, the bandwidth saving compared to the raw speech transfer is about 36%. The WMN router that faces the highest processor demand, for a particular flow, may spend only close to 10% of the speech processing workload required for a session.