The author characterizes the specificity of the evidence proceeding before the arbitration court, which manifests itself primarily in the distinctness of the evidence proceeding regulated in k.p.c. and the autonomy of the parties’ will to the arbitration in terms of shaping the rules of evidentiary proceeding. The author broadly discusses the issues of arbitration contracts and evidence contracts in the context of the principle of contract freedom and the issues of witness testimonies. The interpretation was made with Art. 1184 k.p.c. according to which: unless a provision of the Act provides otherwise, the parties may agree on the rules and manner of proceeding before the arbitration court. Suppose arbitration contracts in the broad sense (including the so-called evidence contracts) are substantive law institutions. In that case, it should be recognized that the only limitation in shaping the rules of evidence proceeding is Art. 353¹ k.c. and the imperative provisions of k.p.c. regulating proceedings before an arbitration court (Art. 1183-1193 k.p.c.). The freedom of parties and the arbitration court must respect the rules of procedure under Art. 1183 of k.p.c., i.e., the right of the parties to a fair trial, the right to be heard, the principle of equal treatment of the parties, guaranteeing the party the possibility to defend its rights.