The monolayer adsorption of spherical molecules of diameter d on the internal surface of an mth generation Menger sponge MSm of size a as a model substance for a porous body is considered. It is shown that the specific (internal) surface area S of MS. is a highly discontinuous function of the diameter-pore commensurability ratio r = d/a(m), where a(m) = a/3(m) is the edge length of the smallest pore. This implies that the fractal dimension D of the sponge cannot be recovered from the usual log-log plot of S vs. r unequivocally. (C) 2002 Published by Elsevier Science B.V.