Ancient Grecian Government
Ancient Greece was the beginning of democracy. In 507 BC Cleisthenes introduced a new form of government and principle which was "rule by the people" and leaders were elected.
This system was divided into three groups: writers of the laws, a council of representatives from each tribe, and courts where citizens argued cases before randomly-selected jurors.
Ancient Roman Government
Roman government went through many changes during its existence including city state, kingdom, republic, and imperial periods. Its main principle was that of "republic" in which leaders were elected and only for a limited time.
Like the Greeks, the Republican Roman government had three separate branches of government but they operated a little bit differently: legislative (makes laws) with the Senate and assemblies, executive (enforces laws) led by two consuls, and judicial (interprets laws) with eight judges.