It is shown that the encoding/decoding problem for any asynchronous M-user memoryless multiple-access channel can be reduced to corresponding problems for at most 2M-1 single-user memoryless channels. This is done via a method called time-splitting multiple-access which is closely related to a recently developed method called rate-splitting multiple access. It is also related to multilevel coding. The practical interest for time-splitting multiple access is that it reduces the seemingly hard task of finding good multiple-access codes and implementable decoders for such codes to the much better understood task of finding codes and decoders for single-user channels. As a by-product, some interesting properties of the capacity region of M-user asynchronous discrete memoryless channels are derived.