Steady state exchanges between the Arctic shelves and the central basins are estimated using an inverse box model. Estimates based only on mass, heat, and salt conservation are highly uncertain and cannot determine how the shelf-basin exchange is partitioned between dense overflows and surface layer exchange. Inclusion of Δ18O conservation greatly reduces the uncertainty. With the Δ18O constraints, dense water fluxes from the shelves of 0.2¿0.1 Sv in the Canadian Basin and 1.4¿0.3 Sv in the Eurasian Basin with a small (O(0.1 Sv)) surface layer transport from shelves to basins best satisfy the requirements of steady state. Up to 3.8 Sv of shelfbreak upwelling is consistent within error bars with steady state, but none is required. Water leaving the shelves is replaced primarily from the Bering Strait, the Barents Sea inflow, and runoff and not from the basin surface layer; proper representation of these external sources for the shelves is important for capturing the full range of plausible steady solutions. The steady state solutions identify the balances which, if upset, could lead to Arctic change. ¿ 1999 American Geophysical Union