Abstract. In the framework of the International Partnerships in Ice Core Sciences, one of the most important targets is to retrieve an Antarctic ice core that extends over the last 1.5 million years (i.e. an ice core that enters the climate era when glacial–interglacial cycles followed the obliquity cycles of the earth). In such an ice core the annual layers of the oldest ice would be thinned by a factor of about 100 and the climatic information of a 10 000 yr interval would be contained in less than 1 m of ice. The gas record in such an Antarctic ice core can potentially reveal the role of greenhouse gas forcing on these 40 000 yr cycles. However, besides the extreme thinning of the annual layers, also the long residence time of the trapped air in the ice and the relatively high ice temperatures near the bedrock favour diffusive exchanges. To investigate the changes in the O₂ / N₂ ratio, as well as the trapped CO₂ concentrations, we modelled the diffusive exchange of the trapped gases O₂, N₂ and CO₂ along the vertical axis. However, the boundary conditions of a potential drilling site are not yet well constrained and the uncertainties in the permeation coefficients of the air constituents in the ice are large. In our simulations, we have set the drill site ice thickness at 2700 m and the bedrock ice temperature at 5–10 K below the ice pressure melting point. Using these conditions and including all further uncertainties associated with the drill site and the permeation coefficients, the results suggest that in the oldest ice the precessional variations in the O₂ / N₂ ratio will be damped by 50–100%, whereas CO₂ concentration changes associated with glacial–interglacial variations will likely be conserved (simulated damping 5%). If the precessional O₂ / N₂ signal will have disappeared completely in this future ice core, orbital tuning of the ice-core age scale will be limited.