This paper is dedicated to the issues of a legal nature and correlation of special ways of resolving a dispute by the arbitral tribunal — ex aequo et bono (“on the basis of the good and equity”) and amiable compositeur (as an “amicable intermediary”). The paper considers current provisions of resolving a dispute ex aequo et bono and amiable compositeur in the rules of some international arbitration institutions in Russia and Belarus. The authors conclude that the provisions on ex aequo et bono and amiable compositeur should be included in the Russian and Belarussian legislation on international commercial arbitration, formulate them and outline the advantages of such a legislative initiative.