A non-uniform equivalent cable model of membrane voltage changes in branching neuronal trees with active ion channels has been developed. A general branching condition is formulated, extending Rall's 3a2 power rule for passive dendritic trees so that nonuniform cable segments can be treated. The theoretical results support the use of the dendritic pro®le model of Clements and Redman. The theory is then applied to dendrites of dierent morphological type yielding qualitative dierent response behaviour. Key words. Non-uniform equivalent cable ± Dendritic pro®le ± Reduced neuron model ± Dendritic information processing ± Active membrane