A federal appeals court on Monday upheld the government’s largely secret criteria for its no-fly list, which since 2001 has prevented tens of thousands of people from boarding commercial aircraft flying to, from or over the United States.

The list consists of individuals who, in the judgment of the Transportation Safety Administration, present a “reasonable suspicion” that they will commit terrorist acts. It contained 81,000 names as of June 2016 and has been plagued by false positives — the names of children and several members of Congress, including Sens. Ted Kennedy and Ted Stevens.

The agency kept virtually all aspects of the operation secret until 2015, when the Ninth U.S. Circuit Court of Appeals in San Francisco said people barred from flying were entitled to learn whether they were on the list and to receive a summary of the reasons, without revealing classified information.

Four plaintiffs in the same lawsuit — U.S. citizens with no criminal records who have been barred from flying for nine years or more — said federal officials had offered only vague reasons for their continued inclusion on the list.

In one case, the government said only that a man was included on the list because of “concerns” about his travel to Yemen in 2010 and detailed those reasons in information it filed secretly to the court. Another man allegedly told FBI agents he had distributed speeches by a now-deceased terrorist, and a third allegedly admitted he had engaged in militant acts in Somalia — admissions he says were the product of coercive interrogation.

On Monday, the appeals court said the government had gone as far as the law requires in explaining each plaintiff’s listing without breaching national security.

“The government has taken reasonable measures to ensure basic fairness to the plaintiffs, and followed procedures reasonably designed to protect against erroneous deprivation of the plaintiffs’ liberty,” Judge Raymond Fisher said in the 3-0 ruling. Although the freedom to travel is important, he said, “it must be balanced against the government’s urgent interest in combating terrorism.”

Fisher noted that the Supreme Court, in 1984, had upheld a law allowing pretrial detention of juveniles who were considered by officers to pose a “serious risk” of committing a crime before their next court appearance — rejecting a claim that a “prediction of future criminal conduct” was unconstitutionally vague.

Fisher said, each of these plaintiffs had “fair notice” that their alleged conduct, such as traveling abroad for weapons training with organizations linked to terrorism, “would raise suspicion” under the published standards. That was equally true, he said, of the man who traveled to Yemen, based on classified information.

“Where national security concerns arise ... an exact statement of reasons may not always be possible,” Fisher said. He said the court had examined the government’s full explanations for its actions and concluded that “an unclassified summary of the undisclosed reasons was not possible.” And he said plaintiffs’ lawyers may be able to examine all the evidence if they have security clearances, which the lawyers in the current case lacked.

The American Civil Liberties Union, which represented the plaintiffs, assailed the ruling.

“Our clients have been unable to visit family, pursue job opportunities or fulfill religious obligations for over nine years based on vague criteria, secret evidence and unreliable government predictions,” said ACLU attorney Hina Shamsi.

Bob Egelko is a San Francisco Chronicle staff writer. Email: begelko@sfchronicle.com Twitter: @BobEgelko