The dose-volume response of tumours and normal tissues is discussed in terms of 'parallelity' and 'seriality'. The volume dependence of the radiation response of a tumour depends primarily on the eradication of all its clonogenic cells and the tumour has a parallel organization. The response of heterogeneous tumours is examined, and it is shown that a small resistant clonogen population may cause a low dose-response gradient, gamma. Injury to normal tissue is a much more complex and gradual process. It depends on earlier effects induced long before depletion of stem cells or differentiated cells that in addition may have a complex structural and functional organization. The volume dependence of the dose-response relation of normal tissues is therefore described here by a new parameter, the 'relative seriality', s, of the infrastructure of the organ. The model is compared with clinical and experimental data on normal tissue response, and shows good agreement both with regard to the shape of dose-response relation and the volume dependence of the isoeffect dose. For example, the spinal cord has a high and the lung a low 'relative seriality', which is reasonable with regard to the organization of these tissues. The response of tumours and normal tissues to non-uniform dose delivery is quantified for fractionated therapy using the linear quadratic cell survival parameters alpha and beta. The steepness, gamma, and the 50% response dose, D50, of the dose-response relationship are derived both for a constant dose per fraction and a constant number of dose fractions.