The location of the area neutral surface in lyotropic liquid crystalline membranes plays a critical role in the phase behavior of all the mesophases which possess curved interfaces. In this paper a mathematical formalism is developed which allows the experimental determination of the area neutral surface from X-ray structural measurements of the inverse bicontinuous cubic phases. The theory is used to determine the location of the area neutral surface in monoolein (Chung, H.; Caffrey, M. Biophys. J. 1994, 66, 377-381) and didodecyl-beta-D-glucopyranosyl-rac-glycerol (Turner, D. C.; Wang, Z.-G.; Gruner, S. M.; Mannock, D. A.; McElhaney, R. N. J. Phys. II Fr. 1992, 2, 2039-2063). The results indicate that the area neutral surface is located between the C-1 and C-2 positions on the hydrocarbon chains. However, the X-ray and gravimetric data currently available on these systems appears to be of too low a precision to allow one to check for the presence of any net stretching. An error analysis of the theory is used to provide an outline prescription for a new generation of experiments which will allow us to determine the presence of stretching bicontinuous cubic phases.