Big financial institutions located in countries of their origin are able to undermine the country´s financial stability and other countries stability as well. Therefore, they should be regulated both on national level and international levels (Part 1. and 2.) Systemic risk, different approaches to systemic risk measurement and criteria of systemic importance are analysed and different approaches examined (Part 3.) Selected topical problems of SIFIs regulation are dealt with (Part 4.). The author is sceptical on the possibility of SIFIs international regulation; at present a close international co-operation and co-ordination is the only way how to reduce potential risks stemming from the SIFIs two-fold role in the world financial architecture (Part 5.)