Performance evaluation of the 802.11 MAC protocol is classically based on the decoupling assumption, which hypothesizes that the backoff processes at different nodes are independent. A necessary condition for the validity of this approach is the existence and uniqueness of a solution to a fixed point equation. However, it was also recently pointed out that this condition is not sufficient; in contrast, a necessary and sufficient condition is a global stability property of the associated ordinary differential equation. Such a property was established only for a specific case, namely for a homogeneous system (all nodes have the same parameters) and when the number of backoff stages is either 1 or infinite and with other restrictive conditions. In this paper, we give a simple condition that establishes the validity of the decoupling assumption for the homogeneous case. We also discuss the heterogeneous and the differentiated service cases and show that the uniqueness condition is not sufficient; we exhibit one case where the fixed point equation has a unique solution but the decoupling assumption is not valid.