Officials with the race track said one of them weakened between two horses during the race and was vanned off after breaking down.
The other bumped another horse at the start of the race, sticking it through to the finish line, but collapsed after being unsaddled.
Both of the horses were four years old.
Horse racing has been under the microscope since 37 horses died at Santa Anita racetrack in Arcadia during the most recently concluded racing season.
37th horse dies at Santa Anita Park after sustaining leg injury during last race of Breeders' Cup
City News Service contributed to this report.