Described the development trends of the national and regional e-infrastructures in Moldova and in Eastern Partnership (EaP) countries for effective support of research and educational activities. Considering important initiatives, approaches and solutions for development of modern eInfrastructure resources for providing specific services to the research and educational communities in Moldova and other EaP countries. The transition of the traditional science and higher education to e-Science and e-Education is fueled by the ever increasing needs to have access, process and visualize of exceedingly large amounts of data that can‘t be managed without modern communication and computing instruments. eInfrastructure designates a new generation of integrated ICT based resources, services and is widely considered as a key enabler for intensification of research and educational activities. Such infrastructures represent a distributed medium based on high-bandwidth networks, distributed computing resources, High Performance Computing (HPC) and respective data repositories. Special attention is focused on description of implementation of new Cross Border Fibers (CBF) connections in the region, other components of the einfrastructures in the framework of the UE EaPConnect project. Created networking infrastructure is the basis for deployment and operation of national and regional e-Infrastructures that are providing wide range of specific services for universities and research centers. Argued importance of developing of Research and Educational networks as a key e-Infrastructures‘ enables. Described outcomes of regional and national projects in the area of e-infrastructures and modern services deployment for research and education.