Elaboration of a modern Earth system model (ESM) requires incorporation of ice sheet dynamics. Coupling of an ice sheet model (ICM) to an AOGCM is complicated by essential differences in spatial and temporal scales of cryospheric, atmospheric and oceanic components. To overcome this difficulty, we applytwo different approaches for the incorporation of ice sheets into an ESM. Coupling of the Antarctic ice sheet model (AISM) to the AOGCM is accomplished via using procedures of resampling, interpolation and assigning to the AISM grid points annually averaged meanings of air surface temperature and precipitation fields generated by the AOGCM. Surface melting, which takes place mainly on the margins of the Antarctic peninsula and on ice shelves fringing the continent, is currently ignored. AISM returns anomalies of surface topography back to the AOGCM. To couple the Greenland ice sheet model (GrISM) to the AOGCM, we use a simple buffer energy- and water-balance model (EWBM-G) to account fororographically-driven precipitation and other sub-grid AOGCM-generated quantities. The output of the EWBM-G consists of surface mass balance and air surface temperature to force the GrISM, and freshwater run-off to force thermohaline circulation in the oceanic block of the AOGCM. Because of arather complex coupling procedure of GrIS compared to AIS, the paper mostly focuses on Greenland.