A special election was held in on August 28, 1797, to fill a vacancy created by the resignation of Jeremiah Smith (F) on July 26 of the same year. Smith had been appointed United States Attorney for the District of New Hampshire.
New Hampshire electoral law required a majority for election. As no candidate won a majority on the first ballot, a run-off election was held October 30, 1797
| Candidate | Party | First ballot[1] | Second ballot[2] | ||
|---|---|---|---|---|---|
| Votes | Percent | Votes | Percent | ||
| Peleg Sprague | Federalist | 2,739 | 43.3% | 3,697 | 66.6% |
| Woodbury Langdon | Democratic-Republican | 1,423 | 22.5% | 1,858 | 33.4% |
| Edward Livermore | Federalist | 1,349 | 21.3% | ||
| Others | 811 | 12.8% | |||