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In this paper we develop and examine the operation of a distributed and adaptive transmission-scheduling protocol that supports contention-free link-level broadcast transmissions in mobile, multiple-hop networks. The network adapts quickly after topology changes and only the terminals near a change are required to adjust their transmission schedules. Two key parameters affect the ability of the transmission-scheduling protocol to adapt to changes in connectivity: the rate of connectivity changes and the number of terminals near the connectivity changes. We bound the rate of changes and terminal density within which the adaptive protocols can maintain collision-free schedules with an acceptable level of overhead. While the protocols can operate efficiently if the rate of change is within certain limits, there can be periods during which a large number of changes occur. We also characterize the stability of the protocols after such periods of rapid changes in connectivity and show that the protocol can quickly return to a collision-free transmission schedule.