Because of a religious tradition of building a new imperial palace after the death of the previous monarch, there are many 'ancient' capitals of Japan. Frequently prior to the movement of the capital to these locations either the city did not previously exist or was a small village. For example, Naniwa-kyō, which was the capital for a short time in the mid-8th century, was a small town in what is now modern-day downtown Osaka.
That being said, there are two capitals that stand out in what might be called the ancient period of Japanese history because of the cultural, religious, and political events that occurred in the area, so much so that periods of Japanese history are named after them. The first is Asuka. This captial area hosted no less that a dozen palaces during the 7th century. The second is Nara (Heijō-kyō) which served as the capital for most of the 8th century.
Nara and kyoto were the two ancient capitals
Rome and Constantinople
Two of the state capitals that have at least two or more names in them are, Little Rock which is the capital of Arkansas and Salt Lake City, which is the capital of Utah.
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Two US state capitals with names that end in "U" are Juneau, AK and Honolulu, HI.
Juneau, Alaska and Honolulu, Hawaii
Greece and egyptions
The Republic of Ireland, capital: Dublin Northern Ireland, capital : Belfast
There are only two capitals North of Buenos Argentina. The two capitals are Belgrano and Flores.
Springfield is the capital of Illinois and Frankfort is the capital of Kentucky
Shinto and Buddhism.
Phoenicia was an ancient semetic civilization who had two capitals throughout history: Byblos and Tyre (both in modern day Lebanon).