The article discusses the offensive of restitution demands addressed in recent years to American and European museums. The campaign involves ancient objects in museum collections which originated from illegal excavations and /or were exported from the country of their origin. The drive is conducted by the governments of countries with copious archaeological monuments: Italy, Greece, Egypt, and Turkey, under the slogan of a repatriation of national cultural heritage. The demands are of a dual nature. The first pertain to so-called recent imports of classical works of art purchased by American museums after the 1970 UNESCO Convention on the Means of Prohibiting and Preventing the Illicit Import, Export and Transfer of Ownership of Cultural Property, which the USA ratified in 1983. Long after that date American museums continued to purchase antiquities of unclear origin. The earlier formulated demands of their return, including the most publicized claim made by Italy interested in regaining the Euphronios Krater bought by Metropolitan Museum of Art in 1972, remained ineffective. However, as a result of court action and the media campaign conducted by the Italians against museums in the USA a compromise was reached: 21 antiquities including the Euphronios Krater , will be restored to Italy. In return, the New York-based museum will enjoy a long-term loan of exhibits of equal rank. Similar decisions have already been made by the Getty Museum and the Museum of Fine Arts in Boston. Claims of this sort appear not to threaten European museums, which after 1970 much studied the provenance of the purchased antiquities more carefully. On the other hand, they could be affected by claims concerning objects transferred from their countries of origin in the more distant past. In the USA the case of the movable monuments from Machu Picchu, the Inca fortress discovered in 1911 by Hiram Bingham, an historian from Yale University who entrusted them to the collections of the later Peabody Museum, could become a precedent. The present-day Peruvian authorities are questioning the legality of Bingham's activity and they also threaten to litigate. The third part of the article deals with sculptures from the Parthenon, which since 1816 are part of the British Museum collections; the museum purchased them from Lord Elgin, who in 1801 removed the sculptures from the Acropolis in Athens. For the past thirty years Greece has been demanding the return of the monuments, and once again, emphasis is placed on the significance of the Marbles for the national identity of present-day Greeks. At the moment, the majority of the British, including many politicians and researchers, supports the Greek demands. Demands calling for the reinstatement of monuments, for decades in the collections of great European museums, are of an increasingly political nature. The antiquities in question are treated by the governments of contemporary states primarily as symbols of national identify, and have became prestigious readymades in the political reconstruction of the cultural heritage of the countries from whose territory they came. The article asks what could be done by the traditional 'universal' museums, in the light of this axiologically and politically new situation, widely approved also by Western public opinion and international organizations.