Related Rule
Practice Relating to Rule 157. Jurisdiction over War Crimes
Cuba’s Penal Code (1987) grants Cuban courts jurisdiction over, inter alia, crimes against humanity, human dignity or collective health or prosecutable under international treaties regardless of the nationality of the accused or the place where the crimes were committed as long as the acts in question also constitute crimes where they were committed. 
Cuba, Penal Code, 1987, Article 5(3).
According to the Report on the Practice of Cuba, under Cuban law, criminal jurisdiction generally extends to offences committed by Cuban nationals abroad. 
Report on the Practice of Cuba, 1998, Chapter 6.4.
In 2010, in a statement before the UN General Assembly on the scope and application of the principle of universal jurisdiction, the representative of Cuba stated:
Cuba fully supports the statements made by the Islamic Republic of Iran on behalf of the Non-Aligned Movement and by Chile on behalf of the Rio Group.
Cuba reiterates its concerns about the unilateral exercise of extra-territorial criminal and civil jurisdiction by national courts, not emanating from international treaties or other obligations under international law, including international humanitarian law. In this regard, Cuba condemns the promulgation, at the domestic level, of laws based on political motives and directed against other States.
The 1949 Geneva Conventions introduced the application of universal jurisdiction for violations qualified as grave breaches. In accordance with the relevant article in each [Geneva] Convention States have an obligation to search for persons accused of having committed grave breaches “regardless of their nationality” and to bring such persons before its own courts or hand such persons over for trial to another High Contracting Party. Although the [Geneva] Conventions do not expressly stipulate that their jurisdiction must be exercised no matter where the violation was committed, it is generally understood that they establish universal jurisdiction.
Cuba considers that the regulation of the principle of universal jurisdiction by treaties is essential for its establishment and application. Universal jurisdiction must be supplementary to the national jurisdiction of each State. A statement that the relevant national tribunals are undertaking the prosecution of the perpetrator of such grave breaches should prevent any action on the basis of universal jurisdiction. This would strengthen the principles of collaboration and assistance between States and the Rule of Law at the international level.
Finally, Cuba considers it very important that it is clarified, on the basis of applicable international law, what violations are subject to universal jurisdiction and define the elements for its application. This principle can only be invoked in exceptional circumstances when there is no other way to bring criminal proceedings against those responsible for crimes against humanity, or those the international community decides at the time on the basis of consensus and the establishment of clear rules of international law. 
Cuba, Statement by the representative of Cuba before the UN General Assembly on Item 86: The Scope and Application of the Principle of Universal Jurisdiction, 12 October 2010, pp. 1–2.