The planes – a B-17 Flying Fortress bomber and a P-63 Kingcobra fighter – crashed into each other at around 1.20pm local time.
They were part of the Commemorative Air Force Wings Over Dallas show being held about 10 miles from the city centre.
Officials have not said how many people were on board, but the B-17 usually carries a crew of four or five people, while the Kingcobra has a single pilot.
Dallas Morning News said there were no reported injuries among people on the ground.
Anthony Montoya was among those who saw the two planes collide, telling The Associated Press: “I just stood there.
“I was in complete shock and disbelief.
“Everybody around was gasping. Everybody was bursting into tears. Everybody was in shock.”
Debris from two planes that crashed during an airshow at Dallas Executive Airport lie on the ground, Nov. 12, 2022.
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, describing the planes as having been “pulverised”.
“We were just hoping they had all gotten out, but we knew they didn’t,” she added.
The B-17 was used in daylight bombing raids over Germany during World War Two, while the Kingcobra was used mostly by Soviet forces during the same conflict.
The crash will be investigated by the National Transportation Safety Board, with a team expected to arrive later today.
There have been a number of fatal crashes at US airshows in recent years.
Eleven people were killed in 2011 in Reno, Nevada, after a P-51 Mustang crashed into spectators.
In 2019, a bomber crashed in Hartford, Connecticut, killing seven people.
