Dynamic element matching (DEM) is often applied to multi-bit DACs to avoid nonlinear distortion that would otherwise result from inevitable mismatches among nominally identical circuit elements. Unfortunately, for such a DEM DAC to fully achieve this objective its constituent 1-bit DACs must be free of inter-symbol interference (ISI), i.e., the error from each 1-bit DAC must not depend on prior samples of the DAC's input sequence. This paper provides the first quantitative general analysis of the effects of ISI on the continuous-time outputs of DEM DACs. The analysis provides some surprising insights such as the conclusion that for certain types of DEM the only nonlinear distortion caused by ISI is second-order distortion. The paper also presents a digital pre-distortion technique that cancels the second-order distortion in the DEM DAC's first Nyquist band if information about the 1-bit DAC mismatches is available.