BOSTON >> A federal appeals court overturned all fraud convictions Wednesday of two parents who were found guilty of paying bribes to get their kids into elite universities as part of a sprawling college admissions scandal.

The 1st U.S. Circuit Court of Appeals tossed all convictions against Gamal Abdelaziz and all but one conviction of another parent, John Wilson. The Boston-based appeals court upheld Wilson’s conviction on a charge of filing a false tax return.

A jury in Boston’s federal court found the pair guilty in 2021 of buying their kids’ ways into school as athletic recruits in the first case to go to trial in the so-called “Operation Varsity Blues” scandal that embroiled prestigious universities across the country.

Abdelaziz, of Las Vegas, was accused of paying $300,000 to get his daughter into the University of Southern California as a basketball recruit even though she didn’t even make it onto her high school’s varsity team.

Authorities alleged that Wilson, a former executive at Staples Inc., paid $220,000 to have his son designated as a USC water polo recruit and an additional $1 million to buy his twin daughters’ ways into Harvard and Stanford.

Lawyers for Wilson and Abdelaziz argued that their clients believed they were making legitimate donations and that the admissions consultant at the center of the scandal, William “Rick” Singer, pitched his so-called “side door” scheme as a lawful one. They said they were led to believe their money would go directly to colleges, saying they’re no different than other wealthy parents who make donations to get a boost in the admissions process.

The three-judge panel of the 1st Circuit said the trial judge was wrong in instructing the jury that admissions slot constitutes “property” of the universities under the mail and wire fraud law. The judges found that the government also failed to prove that the parents agreed to join the “overarching conspiracy among Singer and his clients.”

The government was allowed to introduce a “significant amount of powerful evidence related to other parents’ wrongdoing in which these defendants played no part, creating an unacceptable risk that the jury convicted Abdelaziz and Wilson based on others’ conduct rather than their own,” the judges wrote.

The ruling is a blow for prosecutors, who netted more than 50 convictions in the scandal that ensnared prominent businesspeople, celebrities and other wealthy parents across the country. Coaches from schools including Yale, Stanford, Georgetown and the University of California, Los Angeles, admitted to accepting bribes.

A spokesperson for Massachusetts U.S. Attorney Rachael Rollins said her office is reviewing the opinion and assessing its next steps.

Attorneys for Abdelaziz said in an emailed statement that their client “has maintained his absolute innocence from day one and is enormously grateful that the Appeals Court has reversed his unfair conviction.”

“We are pleased to have represented him in this matter and look forward to Mr. Abdelaziz putting this behind him,” attorneys Brian Kelly and Joshua Sharp said.

Noel Francisco, Wilson’s lawyer, said in an emailed statement that the decision “confirms what we’ve known from the beginning —John Wilson’s case is fundamentally different from others in the broader Varsity Blues scandal.”

“His children were all qualified for admission to these schools on their own athletic and academic merits, and none of his money went to enrich any coach but, rather, was directed to the schools themselves,” Francisco said. “We are examining the opinion to determine the appropriate next steps.”

Wilson was sentenced last year to 15 months in prison and Abdelaziz was sentenced to a year behind bars, although the court later agreed that they could remain free while they pursued their appeals.

Both men were convicted of fraud and bribery conspiracy, and Wilson was convicted of additional charges of bribery, wire fraud and filing a false tax return.

The ringleader of the scheme, Singer, was sentenced in January to 3 1/2 years in prison.

Among the most high-profile parents who admitted to charges were “Full House” actor Lori Loughlin and her fashion designer husband, Mossimo Giannulli, who paid $500,000 in bribes to get their two daughters into the University of Southern California as crew team recruits, even though neither of them played the sport. Loughlin served a two-month prison sentence and Giannulli served a five-month sentence.

Others who pleaded guilty include “Desperate Housewives” star Felicity Huffman, who paid $15,000 to boost her older daughter’s SAT scores. Huffman was sentenced to 14 days behind bars.