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Weeks of nationwide demonstrations, in which that chanted demand has echoed in streets across the United States, have made one thing clear: The American police face a crisis of legitimacy. And its consequences reach far beyond policing itself.

Those intent on remaking law enforcement to redress decades of racial injustice would do well to look at the experiences of other countries that have wrestled with just that challenge. So would those who insist that there is no problem to be fixed.

In many ways this moment, grounded in centuries of white supremacy and fueled by the wild political polarization of recent years, could not be more American. But there are other precedents — and they are almost entirely from countries where systematically brutal policing has been used to keep a privileged minority in power.

The conclusion made evident on America’s streets is that policing in the United States is abridging the rights of many of its citizens, and it is making a lie of the constitutional promise of equal protection under the law.

The intensity of police violence in America, the fact that it falls disproportionately on black people and other heavily policed minorities, and the continued impunity for police officers who commit wrongdoing, which has institutionalized the abuse, all add up to a stark challenge for American democracy.

“For these communities, police are how they are interpreting American democracy,” said Vesla Weaver, a Johns Hopkins University political scientist who studies policing and democratic legitimacy in the United States. “They do draw links from their experiences with police to how robust their democratic citizenship is.”

And although poor communities bear the brunt of police violence, black Americans of all walks of life still live under its shadow.

“Here in my home in Cambridge, with no police here in my home, I am still thinking about that,” said Megan Ming Francis, an associate professor at the University of Washington who is currently a visiting associate professor at Harvard.

Crises of police legitimacy are hardly unique to the United States. They have also occurred in places like Northern Ireland, South Africa, Sri Lanka and Myanmar, among others. And while some of their experiences may offer guidance for how the United States could start redressing the problems underlying the current unrest, they also stand in stark warning about the scale of the challenge the United States is facing.

“The police can very quickly lose legitimacy,” said Christopher Rickard, a researcher on policing and politics in Northern Ireland. “It’s very hard to regain it.”

Until recently, mainstream debate has tended to treat police killings as isolated incidents of individual officers’ mistakes or misbehavior by “a few bad apples," rather than predictable consequences of systemic problems. (Those partial to that phrasing seem to have forgotten that the rest of the adage is “spoil the barrel.”)

But in any case, the distinction may be a false one.

In divided societies, failure to restrain so-called bad apples within the police and other security forces “is not a capacity issue but a political choice,” said Kate Cronin-Furman, a lecturer in political science at University College London who has studied abuses in Sri Lanka, Myanmar and the Democratic Republic of Congo.

“What this does is to tell marginalized minorities that they are never safe, that they don’t possess the full panoply of citizenship rights, and that their humanity is always in question,” Dr. Cronin-Furman said.

That offers double protections to the dominant class or group: Police violence preserves their position in the social hierarchy, and by encouraging it through implied permission rather than through explicit top-down orders, those in power maintain plausible deniability about their role in the brutality.

Americans are not used to hearing their country compared to the places that Dr. Cronin-Furman studies. But there is substantial evidence that throughout American history, violent and repressive policing has sent a similar message to black Americans and other minority groups who live in poor, heavily policed neighborhoods — and that it continues to do so today.

In the 1860s and 1870s, Southern states and towns designed policing to ensure that newly freed black people remained economically subjugated and politically excluded from the rights of citizenship, said Dr. Francis, who studies state-sanctioned violence against black Americans.

“They wrote things down, so it’s very clear what they were trying to do,” she said. “This was seen as a way to take away those new citizenship rights.”

Many of those written laws eventually changed, particularly after the end of the Jim Crow era in the South. But police violence has continued to send a message to many black Americans that they do not have full access to the rights and protections of citizenship.

The Portals Policing Project, a study conducted by a team of researchers from Johns Hopkins and Yale Universities, turned shipping containers into temporary meeting spaces and placed them in 12 heavily policed neighborhoods in six American cities. Each was set up with communications equipment so that people could discuss their experiences with those in other container “portals” as if they were sharing the same space.

When the researchers analyzed data from thousands of portal conversations over three years, they found a picture of American life that bore striking similarities to what Dr. Cronin-Furman observed in Asia and Africa.

“Portals participants were actually narrating something akin to an authoritarian enclave,” where police practices stripped them of the most valuable protections of citizenship, said Dr. Weaver, the Johns Hopkins professor, who was one of the lead researchers on the project.

In conversation after conversation, the researchers found, people cited what they knew their rights ought to be, but then expressed how they felt those rights had been stripped away.

They had an official right to privacy, but the police could stop and frisk them at any moment. They had an official right to remain silent, but feared the police would harass or punish them if they did not answer questions. They had an official right to peacefully assemble, but in practice could not walk to a park in a group of three or more people without the police handcuffing and detaining them on suspicion of criminal activity.

“What they’re experiencing is very similar, in the sense of high levels of abandonment and state neglect, alongside high levels of surveillance, looks very much like the political violence in the Jim Crow south,” she said. “It looks very much like authoritarian regimes.”

As the scale of the problems with American policing dawns on the public, there are growing calls for fundamental change. The city of Minneapolis voted last week to dismantle its police department entirely and replace it with a new force and new approach to public safety. Organizations like Black Lives Matter have called for police departments to be defunded and most of their duties reassigned. New York and Los Angeles have already pledged to slash millions from police budgets.

Evidence from other countries suggests that even when there is a political mandate for deep police reform, truly changing approaches has been difficult.

When South Africa’s first free democratic elections swept the apartheid regime from office in 1994, one of the new government’s promises was to reform the feared apartheid-era police. Four years later, in Northern Ireland, the Good Friday Agreement marked the end of four decades of violent sectarian struggle. It, too, promised police review and reforms.

To win legitimacy, the police in South Africa and Northern Ireland needed to move past their reputations as enforcers for white and Protestant political dominance, respectively. Those efforts’ success or failure turned on whether the police would continue their past practices of treating the population as a threat to be managed through overwhelming force, or if they could become more responsive to civilians’ need for protection, eventually winning trust across society.

In South Africa, “police kept the same apartheid-era practices of heavy groups of heavily armed paramilitaries,” said Jonny Steinberg, a lecturer at Oxford University who studies South African policing and politics.

Over time, middle-class and wealthy South Africans turned to private security instead, hiring guards, moving to gated communities and traveling only in their own cars. The poor, who could not afford such measures, were left vulnerable.

“What the U.S. can learn is negative,” Dr. Steinberg said. “It’s a paradigm case of how not to police a poor urban population.”

It is a lesson that many American departments have yet to absorb. Indeed, paramilitary-style tactics, often involving military equipment acquired through government surplus programs, have become more popular in the United States in recent years.

“The American police, in the last couple of decades, have deployed themselves in a threatening manner,” said Tom Tyler, a Yale Law School professor who studies policing and government legitimacy. Internally and externally, they have cultivated an image of themselves as warriors prepared to use force against a dangerous population, rather than guardians of their communities.

The language of war and threat was on prominent display in a letter that Ed Mullins, the leader of New York City’s largest police union, sent to officers last week. “We will win this war on New York City,” he wrote. “It’s good against evil and good always wins.”

In Northern Ireland, by contrast, the police did shift away from many of the more militarized counterinsurgency tactics they used during the Troubles. But even now, more than two decades after the peace agreement, the police often struggle to persuade crime victims to trust the formal justice system instead of turning to the rough justice that sectarian paramilitary groups offer, Mr. Rickard, the researcher, said.

“It’s been so difficult in Northern Ireland,” the said. “I just can’t imagine how you even start solving some of the structural issues in the United States.”

Addressing those deep issues will inevitably be difficult, said Kanisha Bond, a political scientist at SUNY Binghamton who studies the Black Lives Matter movement and other black mobilizations for social change.

“This is the full force of history being brought to bear, transmitted through contemporary behavior,” she said. “You see protesters, demonstrators, uprisers going to the heart of what they see as a systemic solution. And that is always going to be uncomfortable.”