The feasibility of a full-duplex physical layer, where a node can transmit and receive at the same time in the same frequency, has been established in recent work. Implicitly, most schemes to-date have assumed synchronous operation which allows clean training of all relevant channels. In this paper, we establish the feasibility of asynchronous full-duplex communication. We show that both modes of asynchronous full-duplex can be enabled: (i) where the start of transmission of a packet at a node precedes start of the reception from the same node, and (ii) where the start of reception precedes the start of transmission. We show that the former mode has a better performance, which is in fact comparable to the performance of synchronous full-duplex. Finally, we also show that the active suppression can be complemented by passive suppression with the use of optimal antenna placment on actual devices. An overall suppression of 80dB is shown possible in actual experiments making full-duplex feasible for realistic deployments.