Modern financial markets are characterized by a process of enlarging the activities of financial institutions, mergers and acquisitions, where they assume the character of financial conglomerates. In order to achieve the greatest possible profits and improving overall performance, financial institutions took over the operations and activities of other financial institutions that are not traditionally associated with them. The aim of this paper is to provide insight that is closer to explain a new phenomenon in the financial market, which is related to the process of taking over the activities of insurance companies by banks - Bancassurance and perform some banking services by insurance companies - asurbanking