The paper deals with the diachronic personal identity, defining two fundamental approaches to the problem: realism and anti-realism. The theory of D. Parfit serves as an illustration of anti-realism, while perdurantism as a specific case of realism. Contrary to D. Parfit, perdurantism is able to solve the problem of the split while preserving the realistic position as far as the diachronic personal persistence is concerned. Several problematic aspects of the perdurantism’s realistic position in practice are examined as well. According to the author and contrary to the widespread conviction perdurantism is compatible with responsibility. Nevertheless, there are some un-acceptable consequences concerning punishment and reward.