Traditionally, the Cherokee had a fairly democratic government. It was very decentralized. They did not have a true central government that ruled their whole tribe. Instead, they had a kind of a tribal government that really didn't have much power. The real power was in the town governments. Each town was essentially autonomous.
Within each town, the government was quite democratic. Each town had a chief, but their was also a council in which all adults of both sexes could participate. Decisions were made based on consensus.
It should also be noted that each town had both a peacetime government and a wartime government. These governments did not get involved in each other's spheres. They were completely separate and each held power during the appropriate times.