In Greek mythology Alpheus or Alpheius, or Alpheios (Greek: Αλφειός, meaning whitish) has a number of tales to his name.

1. Alpheus as man. Hunting in the forests of Greece, Alpheus saw Artemis and desired her. He followed her across all of Greece until she came to Letrinoi. There, Artemis and her nymphs smeared their faces with mud. Alpheus, who had decided to rape Artemis could not distinguish between the Goddess and her nymphs. He fled. This episode stands out because Artemis is usually far more savage and lethal with would-be lovers.

2. Alpheus as a river (present Alfeios River) and river-god, thus like most river-gods a son of Oceanus and Tethys. One of Artemis's nymphs was Arethusa and, having failed to win his Goddess, Alpheus fell in love with Arethusa while she was bathing in his waters. But Arethusa, like her Goddess, desired nothing more than to hunt and be free in the forest so she ran from Alpheus. Finally, arriving at the Island of Ortygia she called upon Artemis who transformed her into a stream. Alpheus flowed through Greece and under the ocean until he rose again near to Arethusa and their waters mingled.

There is no need for these two stories to clash, Alpheus the hunter is also Alpheus the river-god.

Pausanias

There is another legend about the Alpheius. They say that there was a hunter called Alpheius, who fell in love with Arethusa, who was herself a huntress. Arethusa, unwilling to marry, crossed, they say, to the island opposite Syracuse called Ortygia, and there turned from a woman to a spring. Alpheius too was changed by his love into the river.

This account of Alpheius to Ortygia. But that the Alpheius passes through the sea and mingles his waters with the spring at this place I cannot disbelieve, as I know that the god at Delphi confirms the story. For when he despatched Archias the Corinthian to found Syracuse he uttered this oracle:

An isle, Ortygia, lies on the misty ocean
Over against Trinacria, where the mouth of Alpheius bubbles
Mingling with the springs of broad Arethusa.

For this reason, therefore, because the water of the Alpheius mingles with the Arethusa, I am convinced that the legend arose of the river's love-affair.