Contained in this paper are the three phase equilibrium conditions of the (ice + clathrate hydrate + guest-rich) vapour in the (nitrogen + water) and the modelled (air + water) systems at temperatures below the freezing point of water. The precise determination of the equilibrium conditions in those systems are of importance for the analysis of the past climate change using the cored samples from the ice sheets at Antarctica and Greenland because the air hydrates keep the ancient climate signals. The mole ratio of the modelled air composed of nitrogen and oxygen is 0.790:0.210. The equilibrium conditions were measured by the batch, isochoric procedure. The temperature range of the measurements in the nitrogen hydrate forming system is (244.05 < T < 266.55) K and the corresponding equilibrium pressure range is (7.151 < p < 12.613) MPa. The temperature range of the measurements in the modelled air hydrate forming system is (242.55 < T < 267.85) K, and the corresponding equilibrium pressure range is (6.294 < p < 12.144) MPa. The data obtained quantitatively compared with the previously reported data. (c) 2013 Elsevier Ltd. All rights reserved.