Following the State Ballot Law Commission’s June 26 ruling that lieutenant governor candidate Anne Manning Martin, of Peabody, and attorney general candidate Michael Walsh, of Lynnfield, will not have their names printed on the Republican State Primary ballot due to fraudulent signatures, both candidates filed appeals.

In separate court filings, Manning Martin and Walsh argued the commission committed legal and procedural errors when it invalidated enough signatures from their nomination papers to leave each below the required 10,000 certified signatures needed to qualify for the Sept. 1 Republican primary ballot.

The commission determined that Manning Martin filed 10,692 certified signatures, and Walsh filed 10,677, but concluded that each campaign had submitted enough invalid signatures to fall short of the qualifying threshold.

The decisions stemmed from objections filed by Massachusetts Democratic Party Executive Director Adam Roof, and, in Manning Martin’s case, Republican Shawn Oliver, who is also vying for lieutenant governor.

During the hearings, the commission heard testimony that hundreds of signatures collected in Weymouth appeared in the same order as voter lists and, in some instances, matched the order of signatures submitted by other candidates.

The commission also considered evidence involving political consultant Joseph Bronske, who collected signatures for multiple Republican candidates, including Manning Martin and Walsh. According to the commission’s findings, Bronske invoked his Fifth Amendment right against self-incrimination during a deposition and declined to answer questions about whether he forged signatures or knew of anyone who had done so.

Ultimately, the commission invalidated 1,279 of Manning Martin’s signatures, leaving her with 9,413 valid signatures. It also invalidated 1,021 of Walsh’s signatures, leaving him with 9,656 valid signatures.

In her appeal, filed in Essex Superior Court on Wednesday, Manning Martin argued the commission exceeded its authority and violated her constitutional rights by allowing objections she said should have been dismissed on procedural grounds, including issues involving service by certified mail and disclosure of challenged signatures.

She also asserted that the commission relied on evidence that was not properly admitted, prevented her from fully presenting her defense, improperly shifted the burden of proof, and made mathematical errors. Manning Martin further argued even if the disputed signatures were removed, she still exceeded the 10,000-signature requirement and should appear on the ballot.

Walsh raised many of the same procedural objections in his Suffolk Superior Court appeal, which was filed on Tuesday. He argued the commission wrongly accepted Roof’s challenge despite what Walsh maintained were defects in service and filing requirements. He also contended the commission improperly allowed a registered Democrat to challenge a Republican Party’s constitutional right to choose its own nominees without interference from political opponents.

Like Manning Martin, Walsh stated that the commission relied on insufficient evidence and legal errors when it removed him from the ballot.

Separately, on June 18, Walsh also sought emergency relief from the U.S. Supreme Court while the state court challenges continue.

Unless a court overturns the commission’s decisions before ballots are finalized, neither Manning Martin nor Walsh will appear on the Republican primary ballot.