Recent research have considered aeronautical ad hoc networks as a possible mean for future aeronautical communications. By introducing inter-aircraft links, they are supposed to become an alternative to existing solutions based on direct air-ground or satellite links. In this paper, we propose the use of asynchronous Code Division Multiple Access (CDMA) in aeronautical ad hoc networks. We then present a simulation model developed with OPNET Modeler that estimates the impact of Multiple Access Interference (MAI) on packets delivery. Finally, we give the results of some simulations made with an ATC/AOC traffic model, and with real aircraft positions over the French sky.