This talk will describe interactions between the three interpenetrating filamentous networks that are the origin of the stiffness of cells. The three networks are the microtubules, filamentous actin and intermediate filaments. Their mechanical properties can be investigated in detail by using reconstituted networks of the purified proteins, enabling precise measurement of their rheological properties. Here, the properties of a reconstituted three-component, interpenetrating network will be discussed and the role of each of the three component networks will be described. The intermediate filaments have a surprising role as they make a major contribution to the dissipation of the composite network without impacting the stiffness. The corresponding role in the cell will also be described.