Notizen: We predict time-dependent variations in the Earth's precession constant arising from the ice and ocean mass fluctuations associated with the Late Pleistocene glacial cycles. Our predictions incorporate contributions from both the surface mass load redistribution and the adjustment of the solid earth. In this regard, we adopt spherically symmetrical, self-gravitating, Maxwell viscoelastic earth models and obtain results for a large suite of radial viscosity profiles. These profiles include a set obtained from published inferences based on post-glacial relative sea-level and uplift histories, as well as a set intended to sample the sensitivity of the results to variations in the viscosity within a number of major subregions of the mantle (e.g. The transition zone, the upper mantle, and the lower mantle). A more detailed measure of this sensitivity is also obtained by computing Frechet kernels for the predictions. We construct an ice model which incorporates the ICE-3G model for the final deglaciation event and which is constrained to yield a eustatic sea-level variation which matches observed fluctuations in oxygen isotope records over the last 800 kyr. In all cases, the ocean mass redistribution is constrained to be gravitationally self-consistent. The computed Frechet kernels indicate that the predictions are most sensitive to variations in viscosity in the deepest regions of the mantle; indeed, in some cases the sensitivity peaks at the core-mantle boundary. Both positive and negative perturbations to the precession constant are predicted, with the maximum peak-to-peak (relative) variation being ∼0.20 per cent for the published viscosity models and ∼0.32 per cent for all other models. Furthermore, the mean relative perturbation in the precession constant, with respect to the present-day value, is found to reach ∼ -0.08 per cent for the published viscosity models, and ∼ -0.20 per cent for other models. Recent solutions for the Earth's precession, obliquity and insolation parameters (Laskar, Joutel & Boudin 1993), indicate a passage through resonance, associated with a perturbation of Jupiter and Saturn, in the case when the mean relative perturbation in the precession constant is ∼-0.15 per cent. We find that this threshold is not achieved for any of the published viscosity models; however, it is reached, for example, for earth models with lower mantle viscosities which exceed 30–50 × 1021 Pa s, or models characterized by large (∼ two orders of magnitude) jumps in viscosity at mid-lower mantle depths.