Without the absentee ballots, Gimenez would have won 49.5 percent of the vote — short of the 50-percent- plus-one-vote majority required to avoid a runoff against Martinez, who would have garnered 33 percent of the vote.

Candidates had until Monday — 10 days after the election was certified on Aug. 17 — to contest the election. Because the courts were closed Monday while Tropical Storm Isaac passed, the deadline could be extended until Tuesday.

Martinez’s and Garcia’s lawsuits had yet to appear in electronic court records by Monday evening. But Stephen Cody, the attorney representing both men, said he filed the complaints late Friday at the courthouse annex of the South Dade Government Center in Cutler Bay.

Martinez and Garcia are seeking an injunction ordering that the official results contain only early voting and Election Day votes.

There is no bright-line legal standard establishing when a judge can overturn an election. In their complaints, Martinez and Garcia cite a Florida Supreme Court case that says an election may be voided when there is evidence that fraud “permeated the entire process,” even if the number of fraudulent votes would not change the results.

Relying on the same case, a judge voided the 1997 Miami mayoral election between Joe Carollo and Xavier Suarez after 225 illegal votes were cast and hundreds more were found to list false voter addresses, be falsely witnessed or procured by ballot brokers. The trial court ordered a new election.

But the appeals court ruled that voting absentee is a privilege that does not have the same legal protection as voting at the polls, which is a constitutional right.

It proposed a different remedy, saying a new election was not required. Instead, the court ruled that the elections supervisor should toss out all of the absentee ballots and certify the election based on the remaining votes — which is what Martinez and Garcia are asking for now.

“Florida courts have said I don’t need to prove that there are 30,000 corrupt ballots,” Cody said. “All I have to show is that there was a level of corruption in the election sufficient to raise doubts as to whether the election actually put forth the voters’ intent.”

State law, however, has changed since 1997. Voters can now cast absentee ballots for any reason, without citing a medical issue or saying they will be unable to make it to their polling place.

“The Legislature’s spoken, and they eliminated the specific rules that made absentee voting a privilege,” said attorney Kendall Coffey, who represented Carollo in his successful 1997 lawsuit and will now represent Gimenez. “Today, absentee ballots enjoy the same . . . fundamental right as voting in the polling places.”

Miami Herald Staff Writers Scott Hiaasen and David Ovalle contributed to this report.