Ageing is defined as a decline in reproductive and/or somatic performance over time, and as such is experienced by most organisms. Evolutionary theories explain ageing as a consequence of reduced selection pressure against mutations and reduced allocation to somatic maintenance in post-reproductive individuals. In addition, the fecundity of younger age-groups makes a more significant contribution than infinite maintenance of the parental body to the production of subsequent generations. However, in clonal animals, as well as in plants that reproduce by agametic cloning, the adult body is itself a reproductive unit that increases its fitness as a function of genet size. Given the apparent longevity of many such clonal organisms, species undergoing agametic cloning are often assumed to be non-ageing and even potentially immortal. Here, we present a brief overview of ageing in organisms undergoing agametic cloning, focusing on animals and molecular investigation. We discuss molecular and evolutionary aspects of ageing or non-ageing with respect to selection in clonal species. Of particular relevance to the search for potential mechanistic processes behind longevity is the notion that clonal organisms are frequently smaller than their obligate sexual counterparts. In conclusion, we find that while clonal animals also commonly age, evolutionary arguments together with empirical evidence suggest that they are likely to be long-lived and stress resistant at the genet level. However, theoretical modeling continues to predict the possibility of immortality, if the contribution from sexual reproduction is low. Future in-depth study of long-lived clones should present an excellent opportunity to discover novel mechanisms for renewal and long-term somatic maintenance and health.