The modern two-party system consists of the Democratic Party and the Republican Party. Besides the Constitution, Green, and Libertarian parties, there are many other political parties that receive only minimal support and only appear on the ballot in one or a few states.Click to see full answer. Hereof, what is a two party system called?A two-party system is a party system where two major political parties dominate the political landscape. At any point in time, one of the two parties typically holds a majority in the legislature and is usually referred to as the majority or governing party while the other is the minority or opposition party.Also Know, why does the United States have only two major parties? With rare exceptions, members of the two major parties control the presidency, the Congress, the governorships and the state legislatures. In the U.S. system, a party can win a seat only if its candidate gets the most votes. That makes it difficult for small political parties to win elections. Correspondingly, which amendment of the Constitution created the two party system? Twelfth Amendment to the United States Constitution.What are the 6 party systems? First Party System. Second Party System. Third Party System. Fourth Party System. Fifth Party System. Sixth Party System.