Two-party system
Third parties, meaning a party other than one of the two dominant parties, are possible in two-party systems, but they are often unlikely to exert much influence by gaining control of legislatures or by winning elections. While there are occasional opinions in the media expressed about the possibility of third parties emerging in the United States, for example, political insiders such as the 1980 presidential candidate John Anderson think the chances of one appearing in the early twenty-first century is remote. A report in "The Guardian" suggested that American politics has been "stuck in a two-way fight between Republicans and Democrats" since the Civil War, and that third-party runs had little meaningful success.
Third party (United States)
Greens, Libertarians and others have elected state Legislators and local officials. The Socialists had 600 mayors at one time before World War I, including Milwaukee, Wisconsin; New Haven, Connecticut; Reading, Pennsylvania; and Schenectady, New York. There have been 20th Century governors elected as independents, and from such parties as Progressive, Reform, Farmer-Labor, Populist, and Prohibition. There were others in the century before.
However, the United States has had a two-party system for over a century. The winner take all system for presidential elections and the single-seat plurality voting system for Congressional elections have over time created the two-party system (see Duverger's law).