The Hapke theory is used to calculate the emissivity of a semi-infinite layer of granular N-2 ice with CH4 and CO as contaminants. It is assumed that the layer is composed of grains which can be characterized as having a single size, and that temperature gradients in the emitting layers of the surface are negligible. The emission spectrum for beta-N-2, stable above 35.6 K, results from a very broad peak in the absorption spectrum centered at 154 mu m, while two absorption peaks, at 143 and 204 mu m, produce the emission spectrum of the lower temperature alpha-N-2 phase. For a grain size of 1 cm the Planck-mean bolometric emissivity calculated for the pure beta-N-2 ice is 0.85. If the effective N-2 grain size is 1 mm the emissivity is 0.40. Both are low enough to significantly affect surface energy balance calculations. The very narrow absorption features of alpha-N-2 result in even smaller bolometric emissivities of only 0.11 and 0.30 for 1 mm and 1 cm grain sizes at 34 K. The effect of CH4 and CO, in solid solution with N-2 or as separate, intimately mixed grains, on the emissivity is also estimated. It is found that the presence of either or both of these two molecules in solid solution with the N-2 ice on Triton and Pluto only slightly increases the beta-N-2 emissivity. The emissivity of intimate mixtures of grains of CH4 and CO with N-2 is much less certain, and probably much less applicable to Triton and Pluto. CH4 and CO in solid solution with alpha-N-2 increase the emissivity by about 50%. For an alpha-N-2 grain size of 1 cm, the addition of 2% each CH4 and CO in solid solution with the N-2 increases the emissivity from 0.30 to 0.48 at 34 K. For a 1 mm grain size the emissivity of such a solid solution changes to 0.16 from 0.11. However, the emissivity of alpha-N-2 even with CH4 and/or CO in solution is still considerably lower than for beta-N-2. Seasonal variations on Triton and Pluto could be strongly influenced by this emissivity contrast between the alpha and beta phases. In the extreme case of pure N-2 ice, Pluto's atmosphere could be prevented from freezing out, even at aphelion. Copyright (C) 1996 Elsevier Science Ltd