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Six people are dead after two historic military planes collided and crashed to the ground during a Dallas air show, officials say.

Dallas County Judge Clay Jenkins said authorities were working to identify the victims of Saturday's crash, in which two historic military planes collided and crashed to the ground, sending plumes of black smoke billowing into the sky.

"According to our Dallas County Medical Examiner, there are a total of 6 fatalities from yesterday's Wings over Dallas air show incident," he said in a tweet, on Sunday.

Emergency crews raced to the crash scene at the Dallas Executive Airport, about 16 kilometres from the city's downtown.

News footage from the scene showed crumpled wreckage of the planes in a grassy area inside the airport perimeter.

Dallas Fire-Rescue told The Dallas Morning News there were no reported injuries among people on the ground.

Anthony Montoya saw the two planes collide.

"I just stood there. I was in complete shock and disbelief," said Montoya, 27, who attended the air show with a friend.

"Everybody around was gasping. Everybody was bursting into tears. Everybody was in shock."

Officials would not say how many people were on board the planes, but Hank Coates, president of the company that put on the airshow, said one of the planes, a B-17 Flying Fortress bomber, typically has a crew of four to five people.

The other, a P-63 Kingcobra fighter plane, has a single pilot.

No paying customers were on the aircraft, said Coates, of Commemorative Air Force, which also owned the planes. Their aircraft are flown by highly trained volunteers, often retired pilots, he said.

Dallas Mayor Eric Johnson said the National Transportation Safety Board had taken control of the crash scene with local police and fire providing support.

"The videos are heartbreaking," Johnson said on Twitter.

The planes collided and crashed about 1.20pm (6.20am Sunday AEDT), the Federal Aviation Administration said in a statement. The collision occurred during the Commemorative Air Force Wings Over Dallas show.

Victoria Yeager, the widow of famed Air Force test pilot Chuck Yeager and herself a pilot, was also at the show. She didn't see the collision, but did see the burning wreckage.

"It was pulverised," said Yeager, 64, who lives in Fort Worth.

"We were just hoping they had all gotten out, but we knew they didn't," she said of those on board.

The B-17, an immense four-engine bomber, was a cornerstone of US air power during World War II and is one of the most celebrated warplanes in US history.

The Kingcobra, a US fighter plane, was used mostly by Soviet forces during the war. Most B-17s were scrapped at the end of World War II and only a handful remain today, largely featured at museums and air shows, according to Boeing.

Several videos posted on social media showed the fighter plane appearing to fly into the bomber, causing them to quickly crash to the ground and setting off a large ball of fire and smoke.

"It was really horrific to see," Aubrey Anne Young, 37, of Leander Texas, who saw the crash.

Her children were inside the hangar with their father when it occurred.

"I'm still trying to make sense of it."

A woman next to Young can be heard crying and screaming hysterically on a video that Young uploaded to her Facebook page.

Air show safety - particularly with older military aircraft - has been a concern for years.

In 2011, 11 people were killed in Reno, Nevada, when a P-51 Mustang crashed into spectators.

In 2019, a bomber crashed in Hartford, Connecticut, killing seven people. The NTSB said then that it had investigated 21 accidents since 1982 involving World War II-era bombers, resulting in 23 deaths.

Wings Over Dallas bills itself as "America's Premier World War II Airshow," according to a website advertising the event.

The show was scheduled for November 11-13, Veterans Day weekend, and guests were to see more than 40 World War II-era aircraft.

Its Saturday afternoon schedule of flying demonstrations included the "bomber parade" and "fighter escorts" that featured the B-17 and P-63.

Videos of previous Wings Over Dallas events depict vintage warplanes flying low, sometimes in close formation, on simulated strafing or bombing runs. The videos also show the planes performing aerobatic stunts.

The FAA was also launching an investigation, officials said.