Subject of this diploma paper is appointment of arbitrators in arbitration procedure. That procedure is known to mankind since era of the ancient Greeks, and modern arbitration is globally popular way solving disputes out of state courts. It can be conducted as ad hoc arbitration where no competent permament body exists, or as institutional arbitration where conduction of the procedure is handled by some in advanced set up arbitral institution. It is imposed within the procedure itself, as one of the most important parts, selection of suitable arbitrators and their appointment. Parties shall determine whether they want one arbitar or tribunal of three or more members to decide upon their dispute. Besides that, while determing the number of members they have to decide whether they want even or odd number, and adjust further steps according to that. Parties have autonomy to choose a way how to appoint arbitrators. Here they have opportunity to determine who will be chosen arbitrators by themselves or they can pass that role to intermediary. That role can be transferred to some in advanced chosen appointing authority, such in institutional arbitration, or the role can be transferred to appointing authority agreed by parties. During selection parties shall take into account arbitrators impartiality and independence. International Bar Association's Guidelines on Conflict of Interest helps them with that, and these provide detail explanation of circumstances that will make arbitrator partial and dependent. Aside of this requirement parties may agreen some other requests on quality that arbitrator must have. Some of the most important ones are that arbitrator has legal capacity, expertise, knows the language and has different citizenship from parties. In the moment of appointment arbitrator accept certain duties. Duties that are imposed are to disclose any circumstances that may give rise to justifiable doubt in his impartiality and independence, and to conduct the procedure efficiently and fast. Besides that, arbitrator has special duty to keep confidential informations obtained during the procedure as secret. Aside of duties, arbitrators have certain rights from which the most important ones are right on fee for their work and right on indemnity of costs incurred by arbitraion. If arbitrator does not fit under the conditions agreed by parties or conditions issued by applicable law, parties can recall them. If arbitrator is removed from its position, substitute arbitrator will come into his place who will be appointed under the same rules as its antecedent.