Fragment #1 --

Proclus, Chrestomathia, ii:

After the "Returns" comes the "Odyssey" of Homer, and then the "Telegony" in two books by Eugammon of Cyrene, which contain the following matters. The suitors of Penelope are buried by their kinsmen, and Odysseus, after sacrificing to the Nymphs, sails to Elis to inspect his herds. He is entertained there by Polyxenus and receives a mixing bowl as a gift; the story of Trophonius and Agamedes and Augeas then follows. He next sails back to Ithaca and performs the sacrifices ordered by Teiresias, and then goes to Thesprotis where he marries Callidice, queen of the Thesprotians. A war then breaks out between the Thesprotians, led by Odysseus, and the Brygi. Ares routs the army of Odysseus and Athena engages with Ares, until Apollo separates them. After the death of Callidice Polypoetes, the son of Odysseus, succeeds to the kingdom, while Odysseus himself returns to Ithaca. In the meantime Telegonus, while travelling in search of his father, lands on Ithaca and ravages the island: Odysseus comes out to defend his country, but is killed by his son unwittingly.

Telegonus, on learning his mistake, transports his father's body with Penelope and Telemachus to his mother's island, where Circe makes them immortal, and Telegonus marries Penelope, and Telemachus Circe.

Fragment #2 --

Eustathias, 1796. 35:

The author of the "Telegony", a Cyrenaean, relates that Odysseus had by Calypso a son Telegonus or Teledamus, and by Penelope Telemachus and Acusilaus.