The main goal of this paper is to analyze the importance of systemically important banks and their influence on stability of global and national financial systems. Global financial crisis has proved that disorders and failures of systemically important banks have significant negative consequences on stability of financial systems. Due to the lack of money for restructuring systemically important banks, competent authorities accepted preventive regulatory system which commits regulators to identify systemically important banks, Basel 3. In accordance with Basel 3, systemically important banks will be subject of specific regulation with the aim of preventing their failure, which is financially much more effective and rational than bank restructuring and rehabilitation. Croatian National Bank, in order to preserve the stability of Croatian financial system, identifies systemically important banks in its own business environment and imposes them special regulation to reduce the likelihood of their failure because of the huge financial consequences.