The aim of the article is to establish the peculiarities of existing obstacles and promising directions of online education system d evelopment in the context of military conflicts of the present. The research is based on the results of the study of scientific literature in the field of online education during war and the study of practical aspects of this issue. The analytical and bibliographic method was used to conduct the study by studying the scientific literature on the issues of online education in higher education during martial law. An online questionnaire survey of the heads of departments of higher education institutions working with students during military conflicts in the territory of the HEIs was also used. As the heads of departments of higher education noted in their responses, the main obstacles to the development of online education are the lack of development and implementation of educational online platforms, the low rate and quality of creation or adaptation of information technology and e-learning tools. The participants of the survey identified promising areas of development of online learning in higher education during military operations: updating of software and hardware, providing higher education institutions with quality Internet access and distance learning, taking into account current trends in information and educational technologies.

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Within the conditions of rapid development of internationalization processes, the scale of international cooperation between tertiary educational institutions is growing at a quick rate. Currently, the practice of international cooperation between tertiary educational institutions is the most commonly encountered in the form of: international exchange of apllicants of tertiary education (students), teachers (educators), scientists; holding conferences, round tables, symposiums; exchange of information and data on improving the efficiency of the educational process. Therefore, the list of the above mentioned types of international cooperation between tertiary educational institutions is not exhaustive and is constantly updated. Based on the foregoing, the aim of the scientific article is to study the theoretical and practical aspects of international cooperation among tertiary educational institutions in the framework of determining current trends and future prospects for the development of such relations. Methods of analysis, synthesis, observation, description and comparison have been used to disclosure the theoretical and practical aspects of international cooperation among tertiary educational institutions in the framework of determining current trends and future prospects for the development of such relations. The scientific article has discussed and analyzed the dynamics of the students’ mobility from abroad, enrolled in tertiary education, as well as the level of students’ mobility in areas of the corresponding level of higher education in such countries, as: Germany, the Czech Republic and Sweden. The peculiarities of the functioning of the following international networks and university wide projects and platforms have been determined, namely: ACCESS, CALIE, European University Association, Eutopia, Inspireurope, International Association of Universities, MIRAI, Nordic Association of University Administrators, Nordic Centre India, Nordic Centre Fudan University, Nordic Institute of Asian Studies, SGroup European Universities’ Network, SANORD, Scholars at risk, SASUF, which have been formed as a result of international cooperation among tertiary educational institutions. According to the data of the European University Association, it has been established that tertiary educational institutions of Ukraine also take an active part in the system of international cooperation. For instance, 26 tertiary educational institutions of Ukraine act as Individual Full Members and Individual Associate Members of the European University Association. It has been established that the basic areas of international cooperation among tertiary educational institutions include: the development of international mobility in the framework of the exchange not only of students, but also of educators, researchers, and administrative staff; joint teaching and investigation activities; research cooperation.