The increasing spread of cybercrimes and the transboundary nature of cyberspace have presented traditional models of criminal jurisdiction and international cooperation with serious challenges. In many cyber cases, the material element, the harmful outcome, the technical infrastructure, and the identity of the perpetrator and victim are scattered across multiple countries, making it difficult to determine the competent state for prosecution and postponing access to electronic evidence to effective cooperation between states and the private sector. This research, using a descriptive-analytical method and based on a library and document study, explains the conceptual framework of "cybercrimes with an international nature", the principles governing their criminal prosecution, the foundations and conflicts of criminal jurisdiction of states, as well as the mechanisms of judicial and police cooperation in international documents. The 2001 Budapest Convention and recent developments, including the United Nations Convention against Cybercrime, are critically examined in terms of harmonizing criminalization, providing for specific means of obtaining digital evidence, extradition, and mutual legal assistance. The findings show that despite significant progress in strengthening rapid cooperation and specialized networks, conflicts of jurisdiction, slow formal processes, differing human rights standards, and challenges posed by new technologies such as end-to-end encryption and cloud services still constitute significant obstacles to the efficient and rights-based prosecution of cybercrimes of an international nature. Finally, suggestions are made for reforming domestic law, strengthening treaty regimes, and striking a balance between cybersecurity and the protection of fundamental human rights.