Random access schemes for packet networks featuring distributed control require algorithms and protocols for resolving packet collisions that occur as the uncoordinated terminals contend for the channel. A widely used collision resolution protocol is the exponential backoff (EB). New analytical results for the stability of the (binary) EB are given. Previous studies on the stability of the (binary) EB have produced contradictory results instead of a consensus: some proved instability, others showed stability under certain conditions. In these studies, simplified and/or modified models of the backoff algorithm were used. In this paper, care is taken to use a model that reflects the actual behavior of backoff algorithms. We show that EB is stable under a throughput definition of stability; the throughput of the network converges to a non-zero constant as the offered load N goes to infinity. We also obtain the analytical expressions for the saturation throughput for a given number of nodes, N. The analysis considers the general case of EB with backoff factor r, where BEB is the special case with r = 2. We show that r = 1/(1 - e(-1)) is the optimum backoff factor that maximizes the throughput. The accuracy of the analysis is checked against simulation results.