Reno Air Racing Association President Mike Houghton says the two planes landed safely after the mishap about 5 p.m. Thursday. The pilots' names weren't released.
Houghton says that one plane had tail damage and the pilot landed it on its belly.
He says the accident happened during a pylon racing seminar that teaches pilots air racing safety.
The newspaper reports authorities from the Federal Aviation Administration and National Transportation Safety Board are investigating the crash.
The airport is the site of a September 2011 race crash that killed a pilot and 10 others on the ground and injured dozens more.
