Some claim there was a “one-party system” for a brief moment in the Era of Good Feelings under Monroe and the Democratic-Republicans, but that isn’t fully true. There was still federalist opposition in those years.
Factoids tagged with "James Monroe"
George Washington ran without any serious opposition in 1789 and 1792 and James Monroe was re-elected without serious opposition in 1820. Thus, we can say “they ran unopposed” and be mostly correct.