The paper examines the recent trends in international mobility, attractivity for international students, and the number of publications of two universities (Constantine the Philosopher University in Nitra, Slovakia, CPU and Tbilisi State Medical University, Georgia, TSMU) to understand whether the COVID-19 pandemic affected these processes and whether the adverse consequences of the pandemic were still retained after its end. In addition, we examined the influence of EU support for these processes. For this purpose, we analyzed the rates of international mobility (the number of outgoing and incoming students and employees, the number of international students, and the number of publications indexed in SCOPUS and the WoS database of CPU and TSMU before, during, and after the abolishment of administrative restrictions induced by the COVID-19 pandemic. The comparison of CPU and TSMU demonstrated the similarity between these universities in the development of international contacts and cooperation. The indexes of international mobility and the number of publications in the EU university CPU were higher than those in the non-EU TSMU. On the other hand, before COVID-19, the indexes of international mobility and the number of publications of TSMU were stable or tended to decline, but in CPU, they increased. COVID-19 had a negative impact on all indexes of international mobility, but the number of international students continued to increase in both universities, even during the pandemic. The use of home offices during the pandemic promoted an increase in the number of international publications among authors from CPU but not among those from TSMU. After the end of the pandemic, in both universities, the indexes of international mobility increased but sometimes did not return to pre-pandemic levels. In the post-COVID-19 period, in both CPU and TSMU, the number of international students continued to grow, and the number of publications declined. These observations highlight the trend of internalization experienced by both universities, the negative impact of COVID on their international mobility, and the importance of EU support for research.