A simple two-reservoir degassing model for the Earth describes rather well the current degassing rate of 4He which is equal to (3¿1)¿106 cm-2 s-1 according to data for the helium polar wind and the measured 3He/4He ratio. This value of the helium degassing and loss rate provides an important constraint in modeling of noble gases, and some recent models do not fit this constraint. Scaling this value to the known amounts of 40Ar in the atmospheres of Mars and the Earth and to U/K ratios in their surface rocks, this results in a crude estimate of the helium degassing rate on Mars, which is equal to 2.2¿105 cm-2 s-1. Nonthermal escape of He is calculated using the daytime mean atmospheric models for low, mean, and high solar activity with He mixing ratio fHe=1 ppm. Three processes contribute to He escape: (1) electron impact ionization and photoionization above the ionopause followed by solar wind sweeping away of the ions formed (1.3¿105 cm-2 s-1), (2) collisions with hot oxygen atoms formed mainly by recombination of O2+ (2.8¿104 cm-2 s-1), (3) charge exchange of He+ and CO2, N2, and CO between the exobase and ionopause (6¿103 cm-2 s-1). The derived mixing ratio for He is fHe=1.4 ppm for the adopted degassing rate. The He 584 ¿ airglow intensity is equal to 37 R and 67 R at low and high solar activity, respectively. The intensities are 105 R and 240 R for fHe=7 ppm, and 10 R and 16 R for fHe=0.3 ppm. These brightnesses should be detectable using the Extreme Ultraviolet Explorer satellite. The measurement of helium on Mars is important for the determination of the planetary abundance of U and Th, element differentiation in the primordial nebula (by comparison with the Earth and Venus) and in the interior of Mars (by comparison with the U and Th fraction in the surface rocks on Mars measured by the Mars 5 and Phobos orbiters). This measurement makes possible an estimate of the radiogenic heat flux which is important for the thermal balance of Mars' interior. ¿ American Geophysical Union 1993