In 1796, New Hampshire had a single at-large district with 4 seats. Each voter cast 4 votes and a majority of voters (12.5% of votes) was required to be elected. Since only three candidates received a majority, a run-off was held between the candidates in fourth and fifth place to fill the remaining seat.
| District | Incumbent | Party | First elected | Result | Candidates[1] | |
|---|---|---|---|---|---|---|
| Jeremiah Smith | Federalist | 1790 | Incumbent re-elected. | First ballot : √ Jeremiah Smith (Federalist) 25.0% √ Abiel Foster (Federalist) 24.3% √ William Gordon (Federalist) 14.9% Jonathan Freeman (Federalist) 9.5% Peleg Sprague (Federalist) 4.4% Woodbury Langdon (Democratic-Republican) 4.2% John Prentice 4.1% Thomas Cogwell 3.4% Nathaniel Peabody 2.3% John Bellows 2.1% Joseph Cilley 1.9% Nathaniel Rogers 1.9% Second ballot : √ Jonathan Freeman (Federalist) 72.5% Peleg Sprague (Federalist) 27.5% | ||
| Nicholas Gilman | Federalist | 1788/89 | Incumbent retired. New member elected. Federalist hold. | |||
| John Samuel Sherburne | Democratic-Republican | 1792 | Incumbent retired. New member elected. Federalist gain. | |||
| Abiel Foster | Federalist | 1794 | Incumbent re-elected. |