  This paper provides stability and instability conditions for slotted Aloha
under the exponential backoff (EB) model with geometric law $i\mapsto
b^{-i-i_0}$, when transmission buffers are in saturation, i.e., always full. In
particular, we prove that for any number of users and for $b>1$ the system is:
(i) ergodic for $i_0 >1$, (ii) null recurrent for $0<i_0\le 1$, and (iii)
transient for $i_0=0$. Furthermore, when referring to a system with queues and
Poisson arrivals, the system is shown to be stable whenever EB in saturation is
stable with throughput $\lambda_0$ and the system input rate is upper-bounded
as $\lambda<\lambda_0$.
