We develop a new methodology linking 40Ar and 4He degassing to crustal production on Venus in order to examine two different scenarios for the history of magmatism on that planet, both consistent with recent analyses of the cratering record of the Venus surface. The first scenario includes episodic global resurfacing events and modest levels of magmatism between such events, while the second scenario invokes different rates of steady magmatism before and after a given transition time. Our degassing models include distinct mantle, crustal, and atmospheric reservoirs. Diffusive transfer of 40Ar and 4He from the crust to the atmosphere is also taken into account. The 40Ar abundance in the present atmosphere reflects the integrated degassing and magmatism over most of planetary history. In contrast, helium escapes from the planetary atmosphere within a characteristic residence time of 200 Myr to 1.8 Gyr, so the present atmospheric 4He abundance is relevant to the volume of magma produced during the last global resurfacing event and the rate of the magmatism subsequent to that event under the first scenario and to the two steady rates of magmatism and the transition time under the second. Unfortunately, large uncertainties in mineral partition coefficients and in the Ar and He mixing ratios in the lower atmosphere of Venus presently prevent the use of our degassing models to distinguish among crustal formation history models. We therefore explore the influence of these uncertain parameters on the degassing history in order to identify those new laboratory and in situ measurements that will most strongly constrain crustal production history. As an important step in the development of the Ar degassing model, the K budget in the bulk silicate fraction of Venus is re-examined on the basis of Venera and Vega &ggr; ray measurements of K, U, and Th concentrations in surface materials. For U and Th concentrations in the bulk silicate planet of 18--29 ppb and 64--94 ppb, respectively, the degree of mantle melting that formed the surface materials at the Venera 9 and 10 and Vega 1 and 2 landing sites is calculated to lie between 0.02 and 0.16. The degree of melting calculated for materials at each landing site is combined with measurements of surface K concentration to estimate the K concentration in the bulk silicate portion of the planet at between 100 and 300 ppm. These results suggest that Venus and Earth have similar heat production. ¿ 1998 American Geophysical Union