Incumbent Republican Congressman Joseph Rainey of the 1st congressional district, in office since 1870, defeated Democratic challenger John S. Richardson.
The Congress declared the seat for the 2nd congressional district vacant on July 19, 1876, after Charles W. Buttz successfully contested the 1874 election.
Richard H. Cain was nominated by the Republicans for the regular election of the 2nd congressional district and he defeated Democratic challenger Michael P. O'Connor.
Incumbent Republican Congressman Alexander S. Wallace of the 4th congressional district, in office since 1870, was defeated by Democratic challenger John H. Evins.
Incumbent Republican Congressman Robert Smalls of the 5th congressional district, in office since 1875, defeated Democratic challenger George D. Tillman.