The first political party in the United States was known as the "Republican Party" (that's what they chose to call themselves). If you count the Federalists as a political party, it might have been the second. The name is historically correct, but, we can't even use that name anymore without creating confusion. We generally call the first "Republican Party" (the faction led by Jefferson and Madison) the Democratic Republican Party, because the modern Republican Party stole their name. The Same group has also been called the Anti Federalist Party, because they opposed the policy of the group commonly known as the Federalist Party, but this is confusing because these guys were actually federalists, and there was an earlier group which opposed ratification of the Constitution which came to be