Adaptive immunity is commonly viewed as a unique vertebrate feature. A misleading view on vertebrate longevity compared to non-vertebrate animals together with oversimplification of ‘invertebrate’ phylogeny sometimes serves for justifying the limitation of adaptive immunity exclusively to vertebrates. However, here we emphasise that the borderline for differentiation between ‘innate’ and ‘adaptive’ immunity may be fuzzy and artificial. In each taxon, the feature of bearing a particular immunological mechanism should reflect its costs and benefits in a given ecological context. Hence, in invertebrates with a long lifespan some kind of acquired immunity could be expected. Indeed, several recent studies support this view. We therefore stress that the definition of ‘adaptivity’ of immune response should reflect the system function instead of a certain molecular mechanism adopted. If these altered criteria are considered then several pieces of recent evidence indicate that the adaptive immunity in animals might have arisen several times independently and in very different forms.