Update, 4 p.m.: When runoffs were not held in two rural Texas counties that had held primaries in May, the state's election code was violated, according to the secretary of state's office.
The Republican and Democratic parties in Sterling County did not hold primary runoffs on Tuesday even though both hosted primaries in May. In Oldham County, the Republican Party had a primary but no runoff.
By initially holding the primary, the parties were required to follow through and host runoffs, said Rich Parsons, a spokesman for the Secretary of State.
The Secretary of State's office became aware of the possible violation before the runoff and tried to address it, he said.
"As I understand it, attempts were made to contact party officials in both counties to advise them that they were required under the election code to hold runoffs," Parsons said. Those attempts were unsuccessful, he said.
Parsons said someone could contest an election if those counties' votes could have impacted the outcome of a race.
"If someone were to feel that a failure to hold a runoff election were grounds in an election contest, then they could certainly pursue that," Parsons said.
In the past, both the Democratic and Republican parties in Texas have not held primaries in counties where they were unable to recruit party chairs, which are volunteer positions.
"The state party cannot go in and run a county primary or primary runoff," said Texas Republican Party Deputy Executive Director Chris Elam. "That has to be done by a county chairman."
The Texas Republican Party held primaries in all 254 Texas counties this year, the first time the party had achieved that benchmark in over a decade, Elam said.
Democrats didn't hold primaries in 13 counties this year, according to party spokeswoman Rebecca Acuña.
"It's an unfortunate situation that is not as unusual as people might think," Acuña said.
More than 1 million Texas voters participated in Tuesday's primary runoff elections, but none of them were from Sterling and Oldham counties. County clerks with both rural counties confirmed that they did not hold primary runoffs.
"Our Republican chairman had moved out of the county, so he was unable to do it and he was unable to find somebody to take his place in time," said Sterling County Clerk Susan Wyatt said, who added that the Democratic Party chair decided not to hold a runoff as well.
Sterling County, northwest of San Angelo, recorded 327 votes in the May primaries — 315 from Republicans and 12 from Democrats. The county has 864 residents of voting age.
Wyatt said she had to explain to a few Republicans who showed up to the county courthouse in Sterling City that they could not participate in the runoff.
"A few people were not happy about it, but none of them volunteered to step in and be Republican Party chair for this next time," Wyatt said. "Unfortunately when I asked, they would back out the door."
Oldham County, which is in the Panhandle, had county party chairs in place but no interest in holding runoff elections, County Clerk Becky Groneman said.
"We haven't had a runoff election in several years," Groneman said. "The last time we had one, two people voted."
Oldham County recorded 252 votes in the May Republican primary and no votes in the Democratic primary. The county has a voting-age population of 1,354.
Groneman said it was up to County Republican Party Chairman Bruce Voyles to decided to hold a Republican primary runoff election. The party would have had to pay for all expenses except early voting, which would have been covered by the county, she said. Voyles could not be immediately reached for comment.
In the closely watched race for an open U.S. Senate seat, both Oldham and Sterling counties' Republican voters strongly favored Lt. Gov. David Dewhurst in the May primary. Former Texas Solicitor General Ted Cruz won the Republican primary runoff Tuesday by more than 150,000 votes.