WASHINGTON — The Supreme Court on Monday waded into a freedom of speech case resulting from an arrest at Arctic Man, a snowmobile and ski race event that draws thousands to a remote campsite in Alaska.

Justices heard arguments in a case with the potential to affect people who might sue police over claims they were arrested as retaliation for something they said or wrote that’s protected by the First Amendment.

Justice Samuel Alito described the possible cases as ranging from someone who is arrested after insulting an officer arriving at the scene of a dispute to a journalist who writes a story critical of a police department and is later pulled over for speeding.

Alaska resident Russell Bartlett was arrested at the 2014 Arctic Man, a dayslong event held annually in Alaska’s remote Hoodoo Mountains. Chief Justice John Roberts noted that policing Arctic Man is a challenge. He described the event as “10,000 mostly drunk people in the middle of nowhere” and only a handful of Alaska troopers.

The sides dispute whether Bartlett was drunk, but he was arrested for disorderly conduct after exchanging words with two troopers investigating underage drinking. Bartlett first declined to talk to one trooper and later loudly told a second to stop talking to a teenager.

The charges against Bartlett were ultimately dismissed because of budgetary constraints. But Bartlett sued, claiming his arrest was retaliation for comments he made to the officers. A trial court dismissed Bartlett’s lawsuit, saying he was barred from suing because officers had reasonable grounds to arrest him. An appeals course reversed that decision.

A ruling for Bartlett would make it easier to bring such cases, and on Monday several justices seemed interested in allowing at least some similar suits. Justice Stephen Breyer suggested what he called a compromise that would bar suits such as Bartlett’s when police have reasonable grounds for an arrest, unless there is “objective evidence” of retaliation.

Among the groups supporting Bartlett are numerous First Amendment and media organizations, including The Associated Press.

The case follows a similar one the justices heard last term involving a man arrested during a city council meeting in Riviera Beach, Florida. Like Bartlett, Fane Lozman claimed his arrest was retaliation, in his case for being an outspoken critic of the city. The court sided with Lozman, but the ruling doesn’t apply to a broad set of cases.

The case is 17-1174, Nieves v. Bartlett.