The texts known as the "Sibylline oracles" were collected between the second century BCE and seventh century CE. They derive their name from Sibyl, a word indicating a prophetess; there were some ten or twelve of these ladies and there is some evidence that during the reign of Alexander the Great, Sibylline oracles were circulating that referred to the campaigns of the Macedonian king.
The collection we possess, fourteen oracles and several fragments, was written by Jewish and Christian authors, but there are older elements in it: prophetic utterances from earlier times. One of the most tantalizing pieces can be found in the third oracle, lines 381-397, which can here be read in the translation of J.J. Collins.
But Macedonia will bring forth a great affliction for Asia,
and a very great grief for Europe will spring up
from the race of Cronos, the progeny of bastards and slaves.note[Alexander claimed descend from the god Zeus Ammon; Zeus was the son of Cronos.]
Shenote["She" refers to the grief.] will conquer even the fortified city of Babylon.
Having been called the mistress of every land which the sun beholds,
she will perish by evil fate,
leaving a name among her much-wandering posterity.
Also at a certain time there will come to the prosperous land of Asia
a faithless man clad with a purple cloak on his shoulders,
savage, stranger to justice, fiery. For a thunderbolt beforehand
raised him up, a man. But all Asia will bear
an evil yoke, and the earth, deluged, will imbibe much gore.
But even so Hadesnote[The Underworld.] will attend him in everything
though he knows it not.
Those whose race he wished to destroy.
by them his own race will be destroyed.
Yet leaving one root, which the destroyer will also cut off
from ten horns, he will sprout another shoot on the side.note[The "ten horns" are a reference to Daniel 7.7.]
There is no doubt that these words refer to Alexander the Great. The problem is when they were written. Some scholars have claimed that these words were written by a Persian or a Babylonian author during or immediately after Alexander's life. If true, that would be very interesting, because we would have non-Greek evidence that Alexander called himself "son of Zeus Ammon" and was considered the collaborator of the opponent of the Persian supreme god Ahuramazda, a devilish creature named Angra Mainyu, "the hostile spirit" or - in this oracle - Hades.
At first sight, this seems probable, but it is not. One argument against an early date of this fragment is that the words "ten horns" are a clear allusion to the biblical book Daniel, verse 7.7; this book was composed in the second century BCE. This argument is not conclusive, however.
A more convincing argument for a late date is the context. The third Sibylline oracle was composed between 163 and 145 in Egypt and deals with an Egyptian king who could be the Messiah. Later, a large fragment (lines 350-488) was inserted in this oracle; it is devoted to the conflict between "Egypt" and "Asia" on the one hand and "Rome" on the other, and was written shortly before the naval battle of Actium (31 BCE). It includes a reference to a queen who can be identified with the famous queen Cleopatra. Our fragment belongs to this addition and can therefore confidently be dated in the first century BCE.
That the lines quoted above belong to a fourth- or early third century text, was first defended by S.K. Eddy in a book called The king is dead. Studies in the Near Eastern resistance to Hellenism (1961); his arguments were, however, refuted by J.J. Collins in the chapters devoted to the Sibylline oracles in the work mentioned below.
In her History of Zoroastrianism, vol.III (1991), Mary Boyce - the grand old lady of Zoroastrian studies - makes a very strange mistake. Although she quotes the translation of Collins and must therefore be aware of his objections to Eddy's ideas, she accepts the latter's interpretation. Of course a scholar may stick to an outmoded point of view or hold a minority position, but the least Boyce should have done was indicate this more clearly. As it now stands, her words are misleading. One of those who were misled, was Michael Wood in his In the footsteps of Alexander the Great (1997).
J.J. Collins, "Sibylline Oracles (Second Century BC - Seventh Century AD)" in: James Charlesworth (ed.): The Old Testament Pseudepigrapha, vol. I (1983 New York) pages 223-316