This paper proposes a mathematical framework for evaluating the throughput of an 802.11 distributed wireless network when the system allows multi-packet reception in asynchronous operating mode. Differently from previous studies on multi-packet reception, which assume a certain synchronization between the different sources at the beginning of the respective transmissions, this work theoretically analyzes a fully distributed scenario, where each node can access to the medium in a completely asynchronous way. More precisely, a new transmission can begin in a channel where other nodes are already communicating as long as the current channel load is within a given threshold. The proposed framework consists of a single source, 802.11 specific model, which generalizes a previously presented analytical model, and a novel network model, which is adopted to evaluate the theoretical performance in terms of throughput. The novel model, which includes the synchronous scenario as a particular case, is employed to investigate the influence of the number of allowed communications, of the load threshold, and of the minimum contention window on the network performance. Furthermore, the theoretical analysis is used to evaluate the throughput in presence of Rayleigh fading and noise when error correcting codes are adopted.