Standard measures of ageing i.e. the proportion of older persons in the population and dependency ratios refer to changing proportions between different age groups which result from the changes in the age distribution. However, ageing results in changes of asymmetry of the age distribution as well as in an increase in such characteristics of the distribution like median or mean. A new approach to measurement of ageing, proposed in the article, takes jointly into account these aspects of changes in the age distribution. Starting from the Sundbärg's concept of the age composition for the progressive, stable and regressive populations, different theoretical distributions are defined for the subsequent phases of the demographic transition. Interrelations between an intensity of changes in mortality and fertility can be linked to shifts in asymmetry of the age distribution. Moreover, they are also reflected in different types of ageing: ageing at the bottom without compensation (constant mortality and declining fertility), ageing at the bottom with loss (increasing mortality and declining fertility), ageing at the top with compensation (declining mortality and either constant or declining fertility), ageing at the bottom and at the top with compensation (declining both mortality and fertility). Also different types of the rejuvenation process have been distinguished: rejuvenation without compensation (constant mortality and increasing fertility), with compensation (declining mortality and increasing fertility), rejuvenation with loss (increasing mortality and either constant or increasing fertility). A new measure of ageing, named old-age index, is based on both the mean age and the asymmetry index i.e. is a linear combination of the mean of age and the asymmetry index: S = M (- A + 2) where S is the old-age index, M is the mean of age, and A is the asymmetry index of the age distribution.The new measure used together with the mean age and the asymmetry index allows for a deeper insight into ageing since they account for both a type of ageing and its advancement. To demonstrate usefulness of that proposal two approaches have been used. Firstly, the ageing process in Belgium in the years 1846-2000 has been analysed. Secondly, the cross-country comparison of ageing has been done for 20 countries being in 2000 at different stages of the demographic transition. Results of both approaches illustrate that the new measure taken jointly with the mean age and the asymmetry index reflect more adequately to shifts in the age distribution than the standard measures. The proposed approach to changes in the age distribution provide with information which is useful not only for evaluation of the past changes. It can also be used for a projection purpose.