108 +/- 11 photons of the martian He 584-angstroms airglow detected by the Extreme Ultraviolet Explorer satellite during a 2-day exposure (January 22-23, 1993) correspond to the effective disk average intensity of 43 +/- 10 Rayleigh. Radiative transfer calculations, using a model atmosphere appropriate to the conditions of the observation and having an exospheric temperature of 210 +/- 20 K, result in a He mixing ratio of 1.1 +/- 0.4 ppm in the lower atmosphere. Nonthermal escape of helium is due to electron impact ionization and pickup of He+ by the solar wind, to collisions with hot oxygen atoms, and to charge exchange with molecular species with corresponding column loss rates of 1.4 x 10(5), 3 x 10(4), and 7 x 10(3) cm-2 sec-1, respectively. The lifetime of helium on Mars is 5 x 10(4) years. The He outgassing rate, coupled with the 40Ar atmospheric abundance and with the K:U:Th ratio measured in the surface rocks, is used as input to a single two-reservoir degassing model which is applied to Mars and then to Venus. A similar model with known abundances of K, U, and Th is applied to Earth. The models for Earth and Mars presume loss of all argon accumulated in the atmospheres during the first billion years by large-scale meteorite and planetesimal impacts. The models show that the degassing coefficients for all three planets may be approximated by function delta = delta (0)(t(0)/t)1/2 with delta (0) = 0/1, 0.04, and 0.0125 Byr-1 for Earth, Venus, and Mars, respectively. After a R2 correction this means that outgassing processes on Venus and Mars are weaker than on Earth by factors of 3 and 30, respectively. Mass ratios of U and Th are almost the same for all three planets, while potassium is depleted by a factor of 2 in Venus and Mars. Mass ratios of helium and argon are close to 5 x 10(-9) and 2 x 10(-8) g/g in the interiors of all three planets. The implications of these results are discussed.