A conceptual framework for the center of fundamental education is discussed in view of the already existing experience of the Research and Education Center at M.M. Bogolyubov Institute for Theoretical Physics, created five years ago as an affiliated division of the Institute, and operating on the voluntary basis. This Center offers a basic model for the center of fundamental education, allowing integration between research and education. Such center for fundamental education should aim to guarantee continual education for talented youth in the three phases: school (phys.-math. lyceums), university (students of natural science departments), post-graduate (universities and academy institutes). Staff of the center should include university lecturers, researchers from national academy institutes and abroad, school teachers of physics and mathematics, post-graduates and university graduates. A key recruitment criterion should be engagement in research. To be recruited, university and Academy researchers have to submit joint competitive research projects that can also involve other claimants for positions. About 60% of researchers involved in a project should be recruited full time. Students of the center can be Ukrainians and foreigners who could pass exams on theoretical disciplines. At the same time, they should remain to be students of their HEEs. After graduation of the center (master degree) students get recommendation for post-graduate course. The center should be administered by the research council (distinguished Ukrainian and Western scientists), the executive council (representatives from university departments and Academy institutes which researchers are recruited by the center, and from Ukrainian and foreign sponsors) and the executive director (elected from among the research staff for one year).