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Most previous work on medium access control (MAC) protocols for wireless ad hoc networks has focused on the twin goals of maximising throughput and minimising average packet delay as required for general-purpose applications.In this paper we describe a new MAC protocol for use in multi-hop ad hoc networks whose goal is to provide, with high probability, time-bounded access to the wireless medium for applications with guaranteed response time requirements.The Time-Bounded Medium Access Control (TBMAC) protocol is based on time-division multiple access with dynamic but predictable slot allocation. TBMAC uses a light-weight atomic multicast protocol to achieve distributed agreement on slot allocation and employs location information to minimise contention for slots.TBMAC is the first time-bounded MAC protocol for multi-hop wireless ad hoc networks. In this paper we describe the protocol and provide a number of time bounds for the transmission of messages.