The EUVAC model of the solar EUV flux [Richards et al., 1994> and a recent analysis of terrestrial airglow at the He 584-¿ line by Bush and Chakrabarti [1995> imply an intensity in the center of the solar 584-¿ line which is lower by a factor of 1.8 than that estimated from the model of Tobiska [1991> and used in an earlier analysis of an EUVE observation of the He 584-¿ airglow on Mars [Krasnopolsky et al., 1994>. Two different methods used to select signal from noise in the EUVE observation give Martian effective disk average airglow intensities of 44 and 70 R. To reproduce these intensities with the new solar flux, the helium mixing ratio in the lower atmosphere is required to be 4¿2 ppm. The main escape process from the Martian atmosphere for helium is ionization above the ionopause followed by sweeping out by the solar wind. Our new result for the total escape rate is larger by a factor of 2.8 than the previous EUVE-derived value and is equal to (7.2¿3.6)¿1023 s-1. This escape rate agrees fairly well with the (1.2¿0.6)¿1024 s-1 value determined from Phobos 2 measurements by Barabash et al. [1995>, taking into account the difference in solar activity. Helium is a minor component of the Martian exosphere reaching a fractional abundance of a few percent at some heights. Our models for the formation of 4He and 40Ar by radioactive decay of U, Th, and K and their outgassing from Mars' interior confirm the low degassing from Mars' interior and require a helium outgassing rate which is smaller by a factor 2--4 than the loss rate. The difference may be due to uncertainties of both values, to a possible enhanced outgassing during the last 5¿104 years, to a higher outgassing coefficient of helium than that of argon, and to the contribution of solar wind &agr; particles to the production of helium. Our models show that loss of 40Ar by impact erosion and sputtering was substantial and constituted 75% of the current atmospheric abundance. ¿ American Geophysical Union 1996