The capacity region of frame-synchronous and frame-asynchronous, discrete, two-user multiple-access channels with finite memory is obtained. Frame synchronism refers to the ability of the transmitters to send their code words in unison. The absence of frame synchronism in memoryless multiple-access channels is known to result in the removal of the convex hull operation from the expression of the capacity region. It is shown that when the channel has memory, frame asynchronism rules out nonstationary inputs to achieve any point in the capacity region, thereby allowing only coding strategies that involve cooperation in the frequency domain but not in the time domain. This restriction drastically reduces the capacity region of some multiple-access channels with memory, and in particular the total capacity of the channel, which is invariant to frame asynchronism for memoryless channels.
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