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Adaptive random-access schemes are introduced and analyzed to provide access-control supervision for a multiple-access communication channel. The dynamic group-random-access (DGRA) schemes introduced in this paper implement an adaptive GRA structure. An active terminal transmits its ready packet at random within the next specified time period. Colliding packets are retransmitted at a random slot within the next time period. The duration of each time period is dynamically determined in accordance with the observed state of the channel during the previous time period. Synchronous and carrier-sense asynchronous DGRA procedures, the latter employing collision detection and/or idle detection, are considered. The schemes are shown to exhibit good delay-throughput characteristics. The carrier-sense ADGRA/ID scheme, employing idle detection, is shown to yield superior performance to that exhibited by other carrier-sense schemes, over a wide range of operational parameters.