It is proposed to use random multiple signal levels for channel access in packet broadcast networks. Priority-free random-access protocols that possess that advantage of capture effect are presented. The presented schemes are applied to the slotted ALOHA network, and the performance is analyzed. Closed-form expressions for the system throughput are derived for a general two-signal-level system and a general m-signal-level system. It is shown that the maximum throughput for the two-level system increases from 0. 47 to 0. 52 as the separation between the two levels increases. For the m-level system, the maximum throughput increases from 0. 52 to 0. 66 as m increases. The time-delay characteristic and the throughput-delay tradeoff are analyzed for the simplest two-level system. The results compare favorably with those of the conventional slotted ALOHA system which uses a single signal level for packet transmission. A rotating-priority random access scheme achieving perfect channel utilization is also presented.