Rivers are the dominant source of many elements and isotopes to the ocean. But this input from the continents is not balanced by the loss of the elements and isotopes through hydrothermal and sedimentary exchange with the oceanic crust, or by temporal changes in the marine inventory for elements that are demonstrably not in steady state. To resolve the problem of the observed imbalance in marine geochemical budgets, attention has been focused on uncertainties in the hydrothermal and sedimentary fluxes. In recent Earth history, temporally dynamic chemical weathering fluxes from the continents are an inevitable consequence of periodic glaciations. Chemical weathering rates on modern Earth are likely to remain far from equilibrium owing to the physical production of finely ground material at glacial terminations that acts as a fertile substrate for chemical weathering. Here we explore the implications of temporal changes in the riverine chemical weathering flux for oceanic geochemical budgets. We contend that the riverine flux obtained from observations of modern rivers is broadly accurate, but not representative of timescales appropriate for elements with oceanic residence longer than Quaternary glacial-interglacial cycles. We suggest that the pulse of rapid chemical weathering initiated at the last deglaciation has not yet decayed away and that weathering rates remain about two to three times the average for an entire late Quaternary glacial cycle. Taking into account the effect of the suggested non-steady-state process on the silicate weathering flux helps to reconcile the modelled marine strontium isotope budget with available data. Overall, we conclude that consideration of the temporal variability in riverine fluxes largely ameliorates long-standing problems with chemical and isotopic mass balances in the ocean.