The problem of Athenian naucraries, their places and roles in the political life of Athens applies to the number of discussion problems in historiography of antiquity. This is due to the sporadic nature of information about them, fragmentary and episodicity of the surviving sources, as well as many difficulties associated with the comprehension of information reflected in them, and with its interpretation in a variety of contexts. The paper discusses the etymology of the term ναύκραρος and examines the stories of Herodotus and Thucydides about the suppression of the attempt of the victor of the Olympic games Cylon to establish his tyranny in Athens. Cylon and his supporters were besieged at the Acropolis by the Athenians, who seeing that the siege was dragging on, reassigned the matter, according to Herodotus, to the Prytaneis of the Naucraries, and according to Thucydides – to archons. The following questions are discussed: did the Prytaneis of the Naucraries rule Athens during the Cylonian Affair, as Herodotus says? Or was the power in Athens at that time in the hands of the archons as Thucydides says? Is it possible to somehow reconcile the versions of Herodotus and Thucydides. The conclusion is drawn: despite the fact that the majority of scholars tries to reconcile the versions of Herodotus and Thucydides, the contradiction found in them cannot be resolved convincingly.