Like most river gods, he is a son of Oceanus and Tethys. Telegone, daughter of Pharis, bore his son, the king Orsilochus. Through him, Alpheus was the grandfather of Diocles, and great-grandfather of a pair of soldiers, Crethon and Orsilochus, who were slain by Aeneas during the Trojan War. The river god was also called the father of Melantheia who became the mother of Eirene by Poseidon. In later accounts, Alpheus (Alphionis) was the father of Phoenissa, possible mother of Endymion by Zeus.
According to Pausanias, Alpheus was a passionate hunter and fell in love with the nymph Arethusa, but she fled from him to the island of Ortygia near Syracuse, and metamorphosed herself into a well, after which Alpheus became a river, which flowing from the Peloponnese under the sea to Ortygia, there united its waters with those of the well Arethusa. The well of Arethusa is a symbol of Syracuse. This story is related somewhat differently by the Roman writer Ovid: Arethusa, a beautiful nymph, once while bathing in the river Alfeios in Arcadia, was surprised and pursued by the river god; but the goddess Artemis took pity upon her and changed her into a well, which flowed under the earth to the island of Ortygia. Alpheus took on water form jumping into the stream, but the earth opened and the stream flew underground to appear in a bay near Syracuse, near the island Ortygia, a location sacred to Artemis.
According to other traditions, Artemis herself was the object of the love of Alpheus. Once, it is said, when pursued by him she fled to Letrini in Elis, and here she covered her face and those of her companions (nymphs) with mud, so that Alpheus could not discover or distinguish her, and was obliged to return. This occasioned the building of a temple of Artemis Alphaea at Letrini. According to another version, the goddess fled to Ortygia, where she had likewise a temple under the name of Alphaea. An allusion to Alpheius' love of Artemis is also contained in the fact that at Olympia the two divinities had one altar in common.
In these accounts two or more distinct stories seem to be mixed up together, but they probably originated in the popular belief that there was a natural subterranean communication between the river Alpheios and the well Arethusa. It was believed that a cup thrown into the Alpheius would make its reappearance in the well Arethusa in Ortygia. Plutarch gives an account which is altogether unconnected with those mentioned above. According to him, Alpheius was a son of Helios, and killed his brother Cercaphus in a contest. Haunted by despair and the Erinyes he leapt into the river Nyctimus which afterwards received the name Alpheius.
This article incorporates text from a publication now in the public domain: Smith, William, ed. (1870). "Alpheias". Dictionary of Greek and Roman Biography and Mythology.