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The photonuclear reactions play very important role in both basic and applied nuclear physics research. They are of great interest for study of structure and dynamics of atomic nuclei, nuclear reaction mechanisms, are involved into the research in the field of relativistic heavy ions, astrophysics etc. Absolute majority of photonuclear reaction cross section data has been obtained in experiments using electron bremsstrahlung and quasimonoenergetic photons produced by annihilation in flight of relativistic positrons. Noticeable systematic disagreements between data obtained in various experiments are clearly larger than statistical data uncertainties. The most well-known are the following: i) disagreements of shapes of cross sections obtained using different sources of gamma-quanta: in the whole various reactions cross sections obtained using annihilation photons are much more smooth than those obtained bremsstrahlung; ii) cross sections of partial photoneutron reactions (g, 1n) and (g, 2n) obtained using annihilation photons at Livermore (USA) and Saclay (France) have noticeably (up to 100%) different values: as a rule SIGMA(g, 1n) have larger values at Saclay, but SIGMA(g, 2n) vice versa at Livermore. Many investigations have been carried out to study the reasons of disagreements and to produce the methods for their overcoming. Unfortunately those investigations have not been systematic, have not based on physics criteria of data reliability and therefore the correspondent recommendations were contradictory. For analysis of data reliability objective physical criteria were proposed, the experimentally–theoretical method for evaluation of reaction cross sections satisfied physical criteria was developed and new reliable reaction cross sections were evaluated for many nuclei.