Berryman and Wang (2000) provide a formulation, as well as some specific examples of the predictions, of a double-porosity dual-permeability model for wave propagation in heterogeneous poroelastic media. The analysis is fairly tedious and we do not have space to present details here. The main conclusion of the double-porosity analysis is that the presence of the two porosities and permeabilities leads to new modes of propagation. In particular, bulk compressional and shear waves very similar to those in Biot's single-porosity formulation are found, and now there are also two slow compressional waves. As the choices of parameters are varied, there are many types of interactions among these waves that are possible, but -- in the simplest cases -- each of the two slow waves acts individually like the one described here for single-porosity poroelasticity in the preceding section.