The article examines the principles of mutual trust and mutual recognition in the implementation of judicial cooperation in criminal matters between EU Member States, their correlation with the principles of respect for human rights and fundamental freedoms, the rule of law.

Based on the analysis of doctrinal sources, primary and secondary law of the European Union, and decisions of the Court of Justice of the EU, the evolution of the principles of trust and mutual recognition in the implementation of judicial cooperation in criminal matters between EU Member States is investigated, its stages are highlighted, their characteristic features are identified, the essential characteristics of the principles of mutual trust and mutual recognition are revealed, and the concept of these principles is developed. The relationship between the principles of mutual trust and mutual recognition and the principles of respect for human rights and fundamental freedoms, the rule of law has also been established: when implementing judicial cooperation in criminal cases between EU Member States, the principles of trust and mutual recognition cannot be opposed to the values of the EU – the principles of respect for human rights and fundamental freedoms, the rule of law; the principle of the rule of law and the principle of respect for human rights and fundamental freedoms require the EU Member State not to automatically implement the principle of trust and mutual recognition, but to implement the entire range of measures that make it possible to ensure that in another EU Member State, in the event of the extradition of a person to it, the rights of this person and his fundamental freedoms will not be violated, and the range of these measures is not exhaustive; The implementation of the principles of mutual trust and mutual recognition correlates with the requirement that an EU member state be sure that human rights and fundamental freedoms will not be violated in another EU member state.

The situation regarding appeals by national courts of EU member states to the Court of Justice of the EU regarding the application of the principles of mutual trust and mutual recognition is analyzed. An algorithm of actions is proposed, the application of which allows a state not to violatehuman rights as a value and to prevent its violation by another EU member state, consisting of the following: 1st stage – the implementation by the EU member state of a thorough analysis of the reality of the risk of violation of a fundamental human right by another EU member state; 2nd stage (if such a risk is established) – verification by the national court executing the arrest warrant whether, under the circumstances that have been identified, there is a risk for the person to suffer a violation of human rights.

It is noted that, when integrating with the EU, Ukraine should take measures to strengthen mutual trust between the judicial authorities of the EU Member States and Ukraine. The key to such strengthening lies in the real and effective implementation of the principle of respect for human rights and fundamental freedoms, the rule of law, and in a unanimous understanding of the content of the principles of mutual trust and mutual recognition and not illusory, but real ensuring of their effectiveness in practice without political interference. The strategic ways of properly implementing the principles of mutual trust and mutual recognition in the legislation of Ukraine are as follows: excluding from the legislation of Ukraine the legal norms on the direct prohibition of the extradition of citizens of Ukraine to another state and enshrining provisions that would allow the extradition of a citizen of Ukraine to an EU Member State for his participation in a court session in another EU Member State with subsequent sending back to Ukraine to serve his sentence; defining in the legislation of Ukraine the circle of subjects of the European arrest warrant.

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