To attract foreign investors, around 50 agreements on the promotion and mutual protection of investments has been concluded by the Republic of Kazakhstan, where the parties undertake to create favorable conditions on their territory. By the Decree of the President of the Republic of Kazakhstan of May 19, 2015, the «Astana» International Financial Center was established in the city of Astana, which has been operating since 2016. One of the main tasks of the «Astana» International Financial Center is to attract investment in the sphere of financial services of our country. In addition, with the involvement of excellent judges, and recognized lawyers the «Astana» International Financial Center Court and the International Arbitration Center were established. However, the «Astana» International Financial Center Court does not conduct administrative or criminal proceedings. At the same time, this court has exclusive competence to interpret the acts of the «Astana» International Financial Center. In this connection the question arises about the expediency of consideration of disputes with the state bodies within the framework of the Code of the Republic of Kazakhstan «Administrative Procedural Code of the Republic of Kazakhstan», where the sources of the law of the «Astana» International Financial Center include principles, norms, and precedents of the English law. Are local administrative courts sufficiently qualified to adjudicate disputes under the common law? This article will examine the structure of the «Astana» International Financial Center Court, its jurisdiction, and public-law relations under the current law of the «Astana» International Financial Center, the legislation of the Republic of Kazakhstan.