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According to Farrington (2012) this athlete must have been active between ca AD 156-176. However, Moretti (1953) indicates that this athlete was active in a later period, between ca AD. 212-217. The argumentation of Farrington can be found in his footnote 528. -YP
A mosaic inscription from Rhegium (SEG 55.1056) may refer to him or to his son M. Aurelius Damas (PersonID 1455).
For a detailed study see Strasser 2003 (= Strasser, J.-Y. (2003). ‘La carrière du pancratiaste Markos Aurèlios Dèmostratos Damas’, in Bulletin de correspondance hellénique 127(1): 251-299.)
Weir (2004) also attributes I.Ephesos 1612 to him, as does Moretti (1992), in addition to I.Ephesos 1160.
Not all of his victories have been added to the database yet (April 2020) - CT
Damas was given citizenship of Alexandria by oth emperor Marcus Aurelius and Commodus, as well as made xystarch of multiple games, high priest of the athletic guild and director of the imperial baths. From Septimius and Caracalla he received supervision over the Eusebeia and Sebasta. Moreover, he was able to make his positions of xystarch and high priest hereditary to his sons Aurelius Damas, Marcus Demostratianos, Demostratos Hegemonides and Damianos - all atheltes, as well. (αἰτησάμενος καὶ τυχὼν παρὰ τ[ῶν κυρ]ίων ἡμῶν θειοτάτων αὐτοκρατόρ[ων] Σεουηρου καὶ Ἀντωνίνου την τε ἀρ[χιερω]συνην καὶ τὰς ξυσταρχίας εἰς τὴ[ν τῶν] παίδων διαδοχην). Damas obtained the title of periodoneikes as pankratiast (Gouw). In total, 111-112 victories: Olympia, Delphi (3), Corinth (5), Argos (3+), Rome (3), Puteoli (2), Neapolis (2?), Nikopolis (2), Athens (10), Rhodos (3), Sardis (4), Ephesos (9), Smyrna (6), Pergamon, Alexandria, Larissa (3), Thespiae, Byzantion, Perinthos, Mantinea (3), Sparta (6), Demetrias, Isthmia (7, prize games)