We investigate both theoretically and experimentally the stability of CSMA-based wireless mesh networks, where a network is said to be stable if and only if the queue of each relay node remains (almost surely) finite. We identify two key factors that impact stability: the network size and the so-called “stealing effect”, a consequence of the hidden node problem and non-zero propagation delays. We consider the case of a greedy source and prove, by using Foster’s theorem, that 3-hop networks are stable, but only if the stealing effect is accounted for. On the other hand, we prove that 4-hop networks are always unstable (even with the stealing effect) and show by simulations that instability extends to more complex linear and non-linear topologies. We devise a stabilization strategy that throttles the source and prove that there exists a finite, non-zero rate at which the source can transmit while keeping the system stable. We run real experiments on a testbed composed of IEEE 802.11 nodes, which show the contrasting behavior of 3-hop and 4-hop networks and the effectiveness of our stabilization strategy.