The Democratic-Republican party was a political party founded in 1799 in opposition of the Federalist Party. The founders of the Democratic-Republican party were Secretary Thomas Jefferson and James Madison, who were prime enemies of Hamilton and opposed strong centralized government, which was the purpose of the Federalist party. Instead, the Democratic-Republican party supported the ideology of decentralization, which gave more power to the people.
The Democratic-Republican party dissolved in 1828, around the same time as the Federalist party. The Democratic and Republican parties which exist today are likely to have branched off the ideas of the Democratic-Republican party, though these modern political parties have different ideologies today.