A new method for SANS data analysis which enables one to directly compute the average Gaussian and square mean curvatures of the interface in a bicontinuous porous structure is proposed. We present the analysis of an extensive SANS data set of one-phase bicontinuous microemulsions (18 different CiEj/D2O/n-alkane systems) taken at the minimal specific surface point. Depending on the values of i and j, and the type of oil k, the point of minimal specific surface changes. We interpret the corresponding structural changes in terms of the interfacial curvatures and found that the dependence of the curvatures on i, j, and k could be summarized by a single scaling law, which has a quadratic dependence of the curvatures on the surfactant volume fraction at the minimal specific surface point. (C) 1998 Published by Elsevier Science B.V. All rights reserved.