The Royal Winds are a monarchy---every single one of them are rich nobles; these nobles are collectively known as the Anemoi. Clearly the word "republic" is only for show. If you have an Auldelen Royal wind, you must take a look at this thread.

There are four large families:

Aeolus (the main house) :: saved for plot, can not has takes plzthnx.

Eurus (the east house)
Zephyr (the west house)
Boreas (the north house)
Notus (the south house)

The descendant of the Aeolus family had to choose from someone within these four houses. Whether it be son or daughter, the Aeolus name would remain. The Aeolus name could only be recalled if they discard the name or cause a great deal of dishonor. Those who married into the royal family (let's say, Mrs. Aeolus' husband and child) would also become Aeolus.

This family rules the kingdom under the skies. And, as usual, nobles sit around. The Aeolus Republic is only a country, so there is certainly room for other countries in Neo-Gaea.