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The capacity region of a two-user Gaussian multiaccess channel with intersymbol interference (ISI) in which the inputs pass through respective linear systems and are superimposed before being corrupted by an additive Gaussian noise process is discussed. A geometrical method for obtaining the optimal input power spectral densities and the capacity region is presented. This method can be viewed as a nontrivial generalization of the single-user water-filling argument. It is shown that, as in the traditional memoryless multiaccess channel, frequency-division multiaccess (FDMA) with optimally selected frequency bands for each user achieves the total capacity of the multiuser Gaussian multiaccess channel with ISI. However, the capacity region of the two-user channel with memory is, in general, not a pentagon unless the channel transfer functions for both users are identical.< >