The aim of this diploma thesis is to analyze selected ways of deciding the subject-matter in international commercial arbitration. The thesis is divided into four chapters. The first chapter provides a brief theoretical introduction into the topic and explains the essential terms. The second chapter deals with the institute of amiable compositeur and ex aequo at bono and the third chapter explores lex mercatoria. In these chapters the aforementioned institutes are characterized, their historical development is provided, based on examples from specific countries and institutions the possibilities of their regulation are illustrated, with help of arbitration awards their use in practice is clarified and the importance of these institutes is evaluated. The fourth chapter describes marginal ways of deciding the subject-matter: decision-making based on general legal principles, trade usage, deciding using the method tronc commun, deciding based on Muslim shari’a and eventually, decision-making based on the existence of contracts enabled by the concept of self-regulatory contracts. The thesis tends to confirm or refute these hypotheses - the ways chosen are clearly theoretically defined and limited; these ways are despite their origins and use dependant on national law and they cannot exist without it.