Longtime incumbent Susan Stasny will face Dennis DeWitt in this race.
Stasny, who is seeking her sixth term of office, is being challenged by DeWitt, who oversees the Bee County Community Affairs Department.
Because no Democrat candidate filed for office, the winner of the runoff election will be elected commissioner of Precinct 2 unless a write-in candidate throws a hat into the ring before the November general election.
Also on the ballot is the race for U.S. representative, District 15. Paul B. Haring is challenging Eddie Zamora for the right to face incumbent Democrat Rubén Hinojosa in the fall.
During the March primaries, Haring of Victoria drew the most support with 46.6 percent of all votes cast, compared to 24 percent by Eddie Zamora.
Additionally on the ballot is the race for Supreme Court justice, Place 3, with Rick Green facing Debra Lehrmann.
Only those who voted Republican during the primary or did not vote at all are able to cast a ballet during the runoff. Those voting Democrat or who signed a petition to have a Democrat placed on the ballot are not able to vote during this runoff election.
Regular voting in the runoff election will be Tuesday at these six consolidated polling places:
• Former Bee County Library at 210 E. Corpus Christi St. for Precincts 1, 3 and 10.
• Mineral Baptist Church on Highway 673 for Precincts 2 and 11.
• Pettus Community Center at Bee and Main streets for Precincts 5, 8 and 12.
• Skidmore Fire Station on East Refugio Street for Precincts 4, 6 and 14.
• Police Training Center at 608 W. Milam St. for Precincts 9, 13, 17 and 19.
• Faith Lutheran Church at 1500 Highway 351 for Precincts 16 and 18.