The outgoing speaker, Frederick Muhlenberg, had supported the pro-administration forces during his first two terms, but was elected by a coalition made up mainly of anti-administration members in 1793, and by 1795 he was seen as more favorable to the Democratic-Republicans.

Despite the Democratic-Republican majority, however, Muhlenberg was not re-elected, and was succeeded by Federalist Jonathan Dayton.

In some states, the congressional delegation was not elected until after the legal start of the Congress (on the 4th day of March in the odd-numbered year).

Under New Hampshire's electoral laws, a majority of voters (12.5% of votes) was required for election.

Only three candidates achieved a majority, and so a run-off election was held for the fourth seat.