In this paper, the rationale and some advantages for multiaccess broadcast packet communication using satellite and ground radio channels are discussed. A mathematical model is formulated for a “slotted ALOHA” random access system. Using this model, a theory is put forth which gives a coherent qualitative interpretation of the system stability behavior which leads to the definition of a stability measure. Quantitative estimates for the relative instability of unstable channels are obtained. Numerical results are shown illustrating the trading relations among channel stability, throughput, and delay. These results provide tools for the performance evaluation and design of an uncontrolled slotted ALOHA system. Adaptive channel control schemes are studied in a companion paper. Copyright © by 1975 The Institute of Electrical and Electronics Engineers, Inc.