A federal appeals court on Tuesday questioned whether the alleged union strong-arm tactics that have been the basis for recent federal prosecutions and investigations — including one tied to City Hall — constitute the crime of extortion or whether they fall within the historically protected rights of unions to organize and protest.

“Is this criminal under the Hobbs Act?’’ Judge David J. Barron asked rhetorically, referring to the 1946 law that made it a federal crime to use robbery or extortion to influence interstate commerce.

The appeals court was reviewing the case involving two former Teamsters members, John Perry and Joseph Burhoe, who were convicted in 2014 of Hobbs Act extortion for using the threat of pickets and the disruption of events to persuade event holders to hire union workers. Both men are now serving prison time.

At one point, Barron questioned whether there is a difference between union members seeking available jobs and pushing for an employer to fire people so that union members can be hired in their place.

“Is that OK, or not OK?’’ Barron, one of three judges on the appeals panel, asked one of the defense lawyers.

“That is not an unfair labor practice,’’ responded Michael R. Schneider, who represents Perry.

Miriam Conrad, an attorney for Burhoe, also argued that civil laws under the National Labor Relations Act were better suited to address the union members’ conduct, not the Hobbs Act.

“This is exactly the type of activity Hobbs Act extortion was not intended to reach,’’ she said.

In a string of recent prosecutions of union members, the case is one of the first nationally to be reviewed by an appeals court, and the outcome could set the legal standard for future prosecutions and ongoing investigations.

“It provides the first opportunity to address the difficult dynamic between protections given by the Supreme Court, and the scope of [federal extortion laws],’’ said Martin Weinberg, a Boston lawyer who has followed the local union cases. “This is an important case in part because it has the potential to set a precedent that affects other cases.’’

At issue in the appeal is a landmark 1970s US Supreme Court case — known as the Enmons decision — that protects union members from Hobbs Act prosecutions, as long as their actions are in pursuit of legitimate union objectives. The case involved electrical workers who used violence against a utility company — they blew up a company substation and shot a rifle at transformers — while picketing for a new contract. The court held that they could be charged with the underlying acts in state court, but not federal extortion.

Union workers have protested and picketed under that protection in the decades since, but in recent years, prosecutors in Boston and throughout the country have targeted union workers who use the threat of pickets — and in some cases violence — to intimidate companies that do not have union contracts and no desire to hire union workers.

Prosecutors allege that the union members extorted jobs that were unwanted, superfluous, or fictitious, citing the legal language that was used in the Enmons decision, and said the extortion amounted to payoffs for the union workers.

Ross Goldman, an assistant US attorney, argued at Tuesday’s hearing that the Supreme Court recognized in the Enmons decision that Congress passed the Hobbs Act to address certain types of acts that are not in pursuit of a legitimate union objective — such as the demand for superfluous jobs, as alleged in the Perry and Burhoe case.

“The Supreme Court said the Hobbs Act was specifically written to reach that conduct,’’ he said.

Another Teamsters member, James E. Deamicis, was convicted of similar allegations in a separate trial, and a fourth union member tried with Burhoe was acquitted.

Last year, prosecutors also charged five Teamsters members they allege attempted to extort jobs from the Top Chef television show, which was shooting in Boston.

Prosecutors connected the case to City Hall, alleging that a high-ranking member of Mayor Martin J. Walsh’s administration, Kenneth Brissette, called two Boston restaurants warning them that the union would picket them if they hosted the television show. The disclosure led to questions over whether the administration was inappropriately advocating for the union.

Separately, Brissette and another City Hall official, Timothy Sullivan, were charged with extortion, accused of threatening to withhold permits for the music festival Boston Calling unless organizers hired union workers.

The appeals court review of the Burhoe and Perry case will not affect the cases of Brissette and Sullivan because they are not union members. But it could set the legal framework for the Top Chef case, which is being watched by union leaders and lawyers.

Deamicis, who is appealing his conviction, is also watching. At his sentencing, he told a federal judge he would be vindicated on appeal.

“It’s long been an understanding by unions that they can seek work,’’ said his lawyer, Thomas Iovieno, of Boston, who attended Tuesday’s appeal hearing and called it “a critically important case.’’

“It’s something that’s been done by unions throughout their history,’’ he said.

Milton Valencia can be reached at milton.valencia@globe.com.