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They were airlifted to hospital late into the night.
An eyewitness took a video of the plane taking off.
Smoke trails can be seen as it leaves the tarmac.
It's believed the two pilots are from the Netherlands and Australia.
The Convair-340 plane -- built in 1954 -- was due to soon be flown to the Aviodrome air museum in the Netherlands.
Images from the site showed the plane broken into several pieces.
Civil Aviation Authority spokesman Kabelo Ledwaba said its investigators were at the scene and would issue a statement.
- Additional reporting AFP