US & Canada
13 December 2014
Last updated at 14:45 ET
Both died after encountering police, but grand juries decided not to bring charges, sparking anger and unrest.
A demonstration in New York was also expected to draw thousands.
Organisers arranged buses to take demonstrators to the capital from the length of the US east coast.
The marchers assembled at Freedom Plaza, where they were addressed by activists. They then began to walk down Pennsylvania Avenue, the main thoroughfare linking the White House and the Capitol building.
The mood has been described as calm but defiant, with a large number of police on standby.
At the Capitol, speakers are expected to call for legislative action.
"We need more than just talk," the Rev Al Sharpton, a leading civil rights advocate, said in a statement.
"We need legislative action that will shift things both on the books and in the streets."
The National Association for the Advancement of Colored People, America's oldest civil rights group, is involved in the protest, along with Rev Sharpton's National Action Network and the Urban League.
The event in Washington has been called the Justice for All March, while demonstrations in other parts of the country have been organised under the banner of a National Day of Resistance.
Bereaved families Michael Brown, 18, was shot dead on 9 August during an altercation with a white police officer in Ferguson.
Mr Garner, 43, died while being held down by a white police officer on 17 July.
He had been challenged over the alleged sale of loose cigarettes on a street in Staten Island, New York.
Michael Brown (left) and Eric Garner have become symbols of the protests
The event was caught on camera and his dying plea of "I can't
breathe" has become a slogan of the protesters. It echoes the adoption
of "Hands up! Don't Shoot!" - a Ferguson refrain alleging that Mr Brown
was surrendering to police when the fatal shots were fired.
Relatives of three other black people killed in controversial shootings are also expected to attend the march, according to the National Action Network.
"That message is that all life matters," he said to cheers. "Black life matters. Brown life matters. Yellow life matters. White life matters. And until the federal government does something about it we're gonna march, we're gonna protest, we're gonna lie down, we're gonna sit down, we're gonna stand in the way until we get justice."
New York march co-organiser Umaara Elliott said in a statement that it was "open season on black people".
"Heaven is crying out for justice": Placard held by a protester in Washington DC
Buses were arranged to ferry protesters from New York and other cities
"This stops today": Another slogan of the protest movement
The march in Washington DC is the culmination of weeks of unrest
"So we demand that action be taken at every level of government
to ensure that these racist killings by the police cease," she added.
The decision not to prosecute a policeman over Michael Brown's death sparked riots in Ferguson and as far away as Oakland, California.
However, most of the protests over his and Mr Garner's death have been peaceful and dignified.
Baltimore resident Terry Baisden, 52, told the Associated Press news agency in Washington she was "hopeful change is coming".
She had not protested before, she said, but felt compelled to turn out because "changes in action, changes in belief, happen in numbers".
by Suzanne Gould and Biodun Iginla, BBC News Website
Community leader Martin Baez: "We came here to fight for equal justice"
Thousands
of people have marched through the US capital, Washington DC, to
protest against the recent killings of unarmed black people by police.
Relatives of Michael Brown, shot dead in the Missouri town of
Ferguson, and Eric Garner, who died being restrained in New York, were
due to speak.Both died after encountering police, but grand juries decided not to bring charges, sparking anger and unrest.
A demonstration in New York was also expected to draw thousands.
Organisers arranged buses to take demonstrators to the capital from the length of the US east coast.
The marchers assembled at Freedom Plaza, where they were addressed by activists. They then began to walk down Pennsylvania Avenue, the main thoroughfare linking the White House and the Capitol building.
The mood has been described as calm but defiant, with a large number of police on standby.
Would police body cameras help? Alistair Leithead reports from Rialto, California
"We need more than just talk," the Rev Al Sharpton, a leading civil rights advocate, said in a statement.
"We need legislative action that will shift things both on the books and in the streets."
The National Association for the Advancement of Colored People, America's oldest civil rights group, is involved in the protest, along with Rev Sharpton's National Action Network and the Urban League.
The event in Washington has been called the Justice for All March, while demonstrations in other parts of the country have been organised under the banner of a National Day of Resistance.
Bereaved families Michael Brown, 18, was shot dead on 9 August during an altercation with a white police officer in Ferguson.
Mr Garner, 43, died while being held down by a white police officer on 17 July.
He had been challenged over the alleged sale of loose cigarettes on a street in Staten Island, New York.
Michael Brown (left) and Eric Garner have become symbols of the protests
Relatives of three other black people killed in controversial shootings are also expected to attend the march, according to the National Action Network.
- Akai Gurley, 28, was shot dead by New York police on 20 November
- Tamir Rice, 12, was shot dead in a Cleveland, Ohio, park on 22 November while carrying a pellet gun
- Trayvon Martin, 17, was shot dead on 26 February 2012 by a neighbourhood watch volunteer in Sanford, Florida
"That message is that all life matters," he said to cheers. "Black life matters. Brown life matters. Yellow life matters. White life matters. And until the federal government does something about it we're gonna march, we're gonna protest, we're gonna lie down, we're gonna sit down, we're gonna stand in the way until we get justice."
New York march co-organiser Umaara Elliott said in a statement that it was "open season on black people".
"Heaven is crying out for justice": Placard held by a protester in Washington DC
Buses were arranged to ferry protesters from New York and other cities
"This stops today": Another slogan of the protest movement
The march in Washington DC is the culmination of weeks of unrest
The decision not to prosecute a policeman over Michael Brown's death sparked riots in Ferguson and as far away as Oakland, California.
However, most of the protests over his and Mr Garner's death have been peaceful and dignified.
Baltimore resident Terry Baisden, 52, told the Associated Press news agency in Washington she was "hopeful change is coming".
She had not protested before, she said, but felt compelled to turn out because "changes in action, changes in belief, happen in numbers".
Ferguson shooting
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What happened, and what now?
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Raw fury follows ruling
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As it happened: Protests spread
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How night of violence unfolded
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Grand jury explained
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Violence after grand jury ruling
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Prosecutor's evidence
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