THE observation of apparently simultaneous episodes of deposition or non-deposition of marine sediments in different parts of the world has led to the proposal that at least some sea level rises and falls must be global, or eustatic, in character1-3. Here we show that polar wander of a viscoelastic stratified Earth can induce global sea level fluctuations comparable to the short-term component in the eustatic sea-level curves. The sign of these fluctuations, which are very sensitive to the rheological stratification, depends on the geographical location of the observation point; rises and falls in sea level can thus be coeval in different parts of the world. This finding is in distinct contrast to the main assumption underlying the reconstruction of eustatic curves, namely that global sea-level events produce the same depositional sequence everywhere. This apparent contradiction is due to the poor time resolution of the stratigraphie records in the distant past, which is comparable to the timescale of polar motion4-6, and to non-uniform data coverage. We propose that polar wander should be added to the list of geophysical mechanisms (the others are glacial instabilities, plate tectonic mechanisms, sea-floor spreading, and thermal and compaction-induced subsidence) that can control the third-order cycles in sea level.