The topic of the present scientific article is dedicated to a delicate issue, regarding the bilateral relations of Republic of Moldova and The Ukraine. În 1940, when the border of the two Soviet Republic was settled, many villages and towns populated by Moldovan ethnics, during centuries, have been incorporated into the Ukrainian Republic. The author tries to answer to the question: why the Moldo-Ukrainian border, which now is the border between the two independent countries, was drawn as it was? The answer is that before 1940, starting with the 1918, at the end of the First World War, in diplomatic negotiations, a few European powers supported the idea of transferring of the Northern and the Southern Bessarabia and the Northern Bucovina to Russia or to the Ukraine. However, the Moldovan authorities have now the duty to monitor, to help and support the Moldovan ethnics in their cultural rights, as they live within the historical Moldovan territories which now belong to the Ukraine.