There is this quote from Herodotus about Alexander I, the grandfather of Alexander the Great.
"And that these descendants of Perdiccas are Hellenes, as they themselves say, I happen to know myself, and not only so, but I will prove in the succeeding history that they are Hellenes. Moreover the Hellanodikai, who manage the games at Olympia, decided that they were so: for when Alexander wished to contend in the games and had descended for this purpose into the arena, the Hellenes who were to run against him tried to exclude him, saying that the contest was not for Barbarians to contend in but for Hellenes: since however Alexander proved that he was of Argos, he was judged to be a Hellene, and when he entered the contest of the foot-race his lot came out with that of the first."
Alexander I, hailing from Macedonia is described as unworthy to compete because he is a barbarian and not a Hellen, but he was deemed a Hellen because he proved that he was of Argos. Which leads me to believe that Macedonians at the time, while they shared the Greek language and culture, were not considered Hellenes by the rest of the Hellenes. Nevertheless the fact that his grandfather was judged a Greek and his mother being the daughter of the king of Epirus, still made Alexander the Great a Greek, even if Macedonians were not deemed Hellenes.
