The aim of the article is to analyze the widely spread idea that the late medieval Grand Duchy of Lithuania could unite the whole Rus' and pose an alternative to Moscow. It is shown that the Lithuanian rulers didn't lay such claims; the attempts to detect them in their statements made in 1358 and (allegedly) in 1399 are nothing but misinterpretations. It is also shown that Algirdas, Jogaila and Vytautas had no real chances to subjugate the Duchy of Moscow and its allies and vassals, both as the result of their military expeditions (1368–1372, 1406–1408) and due to the matrimonial union (1383/84).