A typical Wireless Sensor Network (WSN) performs only one action: sensing the environment. The need for smart interaction with the environment has led to the emergence of Wireless Sensor and Actor Networks (WSANs). The evolution from WSNs, which can be thought of to perform only read operations, to WSANs, which can perform both read and write operations, introduces unique and new challenges that need to be addressed. In this context, we identify the problem of mutual exclusion, which is the requirement to act only to the desired level for any particular location and command. We define the different types of mutual exclusion and the associated challenges in the context of WSANs, and show the undesirable consequences of not providing mutual exclusion with example applications. To address this problem efficiently, we propose a greedy centralized approach, and a distributed and fully localized approach based on the centralized approach. Through simulations, we study the performance of the proposed solution with the centralized approach and a baseline strategy, and show that the proposed solution is efficient for a variety of network conditions.