Neuronal dendritic trees exhibit a huge variety of morphologies, and their information processing capabilities are, for the most part, poorly understood. The fundamental difficulty stems from the fact that dendrites can be bewilderingly complicated and appear to operate at a global level; an event in one location potentially influences the entire tree. At first sight, it would seem that the entire tree must be analysed as a single entity unless conceptual simplifications can be introduced. This thesis presents procedures for reducing passive neuronal dendritic tree models to fully equivalent unbranched non-uniform cables. A fully equivalent cable is equivalent in a mathematical sense to the original tree model and capable of reproducing the same physiological behaviour. An understanding of the construction procedures, as well as the results they produce, gives new, and general, insight into the local and global signal processing capabilities conferred on passive dendritic trees by their geometry.