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Cooperative transmission by base stations (BSs) can significantly improve the spectral efficiency of multiuser, multi-cell, multiple input multiple output (MIMO) systems. We show that contrary to what is often assumed in the literature, the multiuser interference in such systems is fundamentally asynchronous. Intuitively, perfect timing-advance mechanisms can at best only ensure that the desired signal components -but not also the interference components -are perfectly aligned at their intended mobile stations. We develop an accurate mathematical model for the asynchronicity, and show that it leads to a significant performance degradation of existing designs that ignore the asynchronicity of interference. Using three previously proposed linear preceding design methods for BS cooperation, we develop corresponding algorithms that are better at mitigating the impact of the asynchronicity of the interference. Furthermore, we also address timing-advance inaccuracies (jitter), which are inevitable in a practical system. We show that using jitter-statistics-aware precoders can mitigate the impact of these inaccuracies as well. The insights of this paper are critical for the practical implementation of BS cooperation in multiuser MIMO systems, a topic that is typically oversimplified in the literature.