The institute of extradition is the oldest form of international legal assistance which has been replaced by the European arrest warrant in Member States of the European Union. Regarding the third countries, such as Bosnia and Herzegovina, extradition is the only instrument enabling the transfer of persons that have to be extradited for criminal trial, imprisonment, or any other measure of deprivation of freedom in the applicant state. In an effort to ensure legal certainty, the principle of legality and the rule of law, states as subjects of international law increasingly regulate their relations in the field of extradition law by signing bilateral agreements in order to achieve that aim. Within this framework, Croatia and Bosnia and Herzegovina concluded the Treaty on Extradition on 28 November 2012. The Treaty was applied temporarily starting from the above date, and it came into force on 6 March 2014. The Treaty regulates the extradition of citizens, departing from the traditional principle of non-extradition of a state’s own citizens. The authors analyse the Treaty on Extradition with a special focus on extradition of a country’s own citizens, especially those with dual citizenship, which is often the case with citizens of Croatia and Bosnia and Herzegovina. Many European and world countries strongly oppose the extradition of their own citizens. The principle of non-extradition of a country’s own citizens is based on the concept of the sovereignty of states and their citizens and their mutual obligations, and it is often a consequence of distrust of judicial systems of other states. However, bearing in mind that the fundamental aim of extradition is the struggle against the absence of punishment for persons suspected or convicted of criminal offences, distrust as a reason for non-extradition should be taken with the greatest caution. The fact that the principle of non-extradition of a state’s own citizens is outdated in modern criminal law is confirmed by the Convention on Extradition between EU Member States according to which extradition cannot be rejected because a person is a citizen of applicant state. The aim of the paper is to draw attention to problems that have an impact on judicial cooperation between Croatia and Bosnia and Herzegovina by analysing the existing normative framework and practical examples of (non)extradition of citizens of one’s own state and offer a contribution to solve these important issues.