Transmission-scheduling protocols can support contention-free link-level broadcast transmissions and delay sensitive traffic in mobile, multiple-hop packet radio networks. Use of transmission-scheduling protocols, however, can be very inefficient in mobile environments due to the difficulty in adapting transmission schedules. The paper defines a new adaptive and distributed protocol that permits a terminal to adapt transmission assignments to changes in topology using information it collects from its local neighborhood only. Because global coordination among all the terminals is not required and changes to transmission assignments are distributed to nearby terminals only, the protocol can adapt quickly to changes in the network connectivity. The two key parameters that affect the ability of the protocol to adapt to changes in connectivity are the rate of connectivity changes and the number of terminals near the connectivity changes. Using simulation, we determine the ranges for these parameters for which our adaptive protocol can maintain collision-free schedules with an acceptable level of overhead. The stability of the protocol is also characterized by showing that the protocol can quickly return to a collision-free transmission schedule after a period of very rapid changes in connectivity. Our channel-access protocol does not require a contention-based random-access phase to adapt the transmission schedules, and thus its ability to adapt quickly does not deteriorate with an increase in the traffic load.