Transgenerational epigenetic inheritance is at variance with the neo-Darwinian theory of inheritance, and this possibly has important implications for how we view evolution, since it could allow for a kind of inheritance of acquired characteristics. We have applied Imre Lakatos and Thomas Kuhn’s models of scientific change and investigated if they can accurately describe the change in the view on inheritance from neo-Darwinism to a view that includes transgenerational epigenetic inheritance, and if so, which model most precisely describes this change. Kuhn views two paradigms as incommensurable and science as non-cumulative, whereas Lakatos does not. Neo-Darwinism views DNA as the only agent of heredity, whereas transgenerational epigenetic inheritance allow for other mechanisms, but despite this important difference, they share much basic knowledge, scientific journals and formal education of their practitioners. We found that both programmes in Lakatos’ model for scientific change were theoretically and empirically progressive, which indicated that none of the programmes should be abandoned. This case fits both Lakatos’ views on incommensurability and the accumulation of knowledge, as well as his view that change in science can be a slow process with programmes competing for years before one of them is abandoned. On this basis we can conclude that Lakatos’ model for scientific change is the best fitting for describing this scientific change in the view on inheritance and thereby evolution.