On the basis of long simulations performed with a three-dimensional climate model, we propose an interhemispheric climate lag mechanism, involving the long-term memory of deepwater masses. Warm anomalies, formed in the North Atlantic when warm conditions prevail at surface, are transported by the deep ocean circulation towards the Southern Ocean. There, the heat is released because of large scale upwelling, maintaining warm conditions and inducing a lagged response of about 150 years compared to the Northern Hemisphere. Model results and observations covering the first half of the second millenium suggest a delay between the temperature evolution in the Northern Hemisphere and in the Southern Ocean. The mechanism described here provides a reasonable hypothesis to explain such an interhemipsheric lag.