The task of stabilizing communication networks sharing a spread spectrum channel is addressed. A slotted system is considered and the stabilization is achieved by controlling the number of packets that are transmitted in every slot. The throughput of the stabilized system is also examined under the constraint that the packet error probability should not exceed a specified value. A comparison with the throughput for an uncontrolled network is also carried out. It is shown that direct sequence spread spectrum systems are capable of achieving a maximum throughput that is larger than the maximum throughput that can be obtained using frequency hopping spread spectrum. Additionally, under the proposed control strategy, the stable network is shown to have a maximum throughput that is close to the maximum throughput for the uncontrolled network. Even more important is the result that with this control access strategy the average number of backlogged packets is very small and the network can be designed to operate below any specified packet error probability.