Two British judges are set to decide on Tuesday whether Julian Assange, the WikiLeaks founder, will be granted the right to appeal an extradition order to the United States, where he is facing charges under the Espionage Act.

Mr. Assange has been held in a London prison since 2019, accused by the United States of violations in connection with the obtaining and publishing of classified government documents on WikiLeaks in 2010.

In April 2022, a London court ordered his extradition to the United States. Priti Patel, Britain’s home secretary at the time, approved the extradition. Last month, two High Court judges heard Mr. Assange’s final bid for an appeal. The judges are expected to hand down a written decision at 10:30 a.m. local time (6:30 a.m. Eastern) on Tuesday.

Here are the most likely scenarios.

Mr. Assange is allowed to appeal.

In this case, Mr. Assange would be allowed to have a full appeals case heard in front of the British court on new grounds. That could opening the door to a new decision about his extradition

This would mean that the legal case, which has caught the world’s attention and mobilized defenders of press freedom, will continue to be disputed, and that Mr. Assange’s removal to the United States will at least be delayed.

The extradition order was initially denied by a British judge in 2021, who ruled that Mr. Assange was at risk of suicide if sent to a U.S. prison. Britain’s High Court later reversed that decision after U.S. officials issued reassurances about his treatment.

A lower-court judge denied Mr. Assange’s request to appeal the extradition order, and his lawyers asked the High Court to overturn that move.

His request is denied.

Mr. Assange could be put on a plane bound for the United States, his lawyers have said, potentially ending his yearslong battle.

But Mr. Assange’s legal team has vowed to challenge an affirmative extradition decision to the European Court of Human Rights in Strasbourg, France. Britain is compelled to comply with the court’s judgment as a signatory to the European Convention on Human Rights. A challenge in the court could potentially pause his extradition until the case is heard in Strasbourg.

Mr. Assange was indicted in 2019 in Northern Virginia on a federal charge of conspiring to hack into a Pentagon computer network in 2010. Then he was indicted on 17 counts of violating the Espionage Act for his role in obtaining and publishing the secret military and diplomatic documents.

The accusations could bring a sentence of up to 175 years in prison on conviction, said his lawyers, who have described the charges as politically motivated. But lawyers for the U.S. government, which has said that the leaks put lives at risk, have said that Mr. Assange is more likely to be given a shorter sentence of four to six years.

Alice Jill Edwards, the United Nations special rapporteur on torture, has said that if he were extradited, Mr. Assange would be at risk of treatment amounting to torture or other forms of punishment.

In a statement last month, she said that Mr. Assange could face “prolonged solitary confinement, despite his precarious mental health status, and to receive a potentially disproportionate sentence.”

American officials previously gave assurances that he would not be held in the United States’ highest-security prison and that, if convicted, he could serve his sentence in his native Australia.

But Ms. Edwards has said that those assurances are “not a sufficient guarantee.”