The transport properties of porous media at low porosities are analyzed. In particular, the electrical conductivity and the permeability are considered. Several experimental results in the literature indicate that conductivity and permeability decrease significantly in the region 5--10% porosity. Recent progress in the theoretical understanding of simple porous media lead to the conclusion that transport ceases at a threshold value of 3% porosity. By modifying the Archie equation and the Kozeny-Carman equation accordingly, one can account for the low-porosity behavior of both conductivity and permeability. ¿ 1999 American Geophysical Union