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A necessary and sufficient condition for a source to satisfy the ergodic theorem and the Shannon-McMillan theorem--the two basic mathematical tools of the Shannon theory--is that it be asymptotically mean stationary (AMS). A channel is defined here to be AMS if whenever an AMS input source is connected to the channel, the resulting input/output process is AMS. We develop several characterizations and properties of AMS channels that resemble those of AMS sources. As an application we show that these ideas are useful in characterizing composite sources, and in particular that there exist sources that exhibit distinct short term and long term stationarity properties. Thus "locally stationary" or "quasi-stationary" processes such as those used to model speech waveforms may also be stationary. In addition, some preliminary results on coding for AMS channels are presented.