The National Football League is bracing for possible widespread player demonstrations during the national anthem at Sunday’s opening games, in what would mark a high-profile escalation of a protest movement over concerns of racial injustice in America.

The games fall on the 15th anniversary of the Sept. 11, 2001, terror attacks, which the NFL plans to commemorate with appearances by military personnel, first responders and two U.S. presidents. That backdrop could further animate a fierce national debate set off last month by quarterback Colin Kaepernick’s refusal to stand for the anthem.

Officials with the NFL Players Association, who have been providing its union members with guidance on what protests are prohibited under the labor agreement, expect that players on several teams may pursue some form of protest.

An official with one team said his organization had prepared a “response plan” for possible protests and expected that most other teams had done the same.

NFLPA spokesman George Atallah said that players can’t violate the dress code—for example, by writing on their helmets—and they can’t interrupt the game. Apart from that, Mr. Atallah said, players can express themselves as they choose.

The league hasn't disciplined Mr. Kaepernick. NFL executive vice president of communications Joe Lockhart said the league has a “somewhat broader” view than the union of what players can and can’t do but explained the league would work together with the NFLPA to deal with the behavior on a case-by-case basis. He said drawing up an exhaustive list of prohibited behaviors wouldn't make sense.

Mr. Kaepernick, the backup quarterback for the San Francisco 49ers, first sat out The Star-Spangled Banner at an August preseason game, saying afterward: “I am not going to stand up to show pride in a flag for a country that oppresses black people and people of color.” Since then, several players have joined Mr. Kaepernick in taking one knee for the anthem, a gesture that has been met with sympathy, solidarity and outrage from fans, commentators and teammates.

The response to Mr. Kaepernick’s protest hasn't only highlighted national anxieties about policing in African-American communities, it has also put coaches and owners in the precarious position of trying to balance respect for players’ political expression against broader public sentiment about the military and police.

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