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This thesis develops the theory needed to determine the throughput and average packet transfer delay of both slotted and unslotted ALOHA networks utilizing multiple received power levels to create beneficial power capture effects in environments where near perfect capture does not occur. The throughput achievable can be greatly increased when two received power levels are utilized. Use of more than two equally spaced power levels provides no significant improvement in the throughput achievable when realistic capture thresholds are considered. The pseudo-Bayesian algorithm used to stabilize slotted ALOHA networks is theoretically adapted to systems employing two power levels.