One set of gloves was worn by Ali when he won the title from Sonny Liston in a huge upset in 1964, while the other set is from his "Fight of the Century" loss at Madison Square Garden in 1971 to Joe Frazier.
Dundee's son, Jim, said the gloves have been stored in a safe deposit box since the fights. They are among more than 100 items that the family is selling in the online sale by SCP Auctions.
"It's kind of bittersweet," Dundee said. "These have been in our possession for nearly 50 years. Dad would bring them home and I would store them."
Angelo Dundee, who was Ali's trainer throughout his career and also trained Sugar Ray Leonard among others, died Feb. 1 at the age of 90.
On Thursday, each set of gloves had been bid up to $241,577. The auction, which also features gloves from Leonard's infamous "No mas" fight with Roberto Duran in 1980 and other Ali memorabilia, ends Friday at SCPAuctions.com
Jim Dundee said money from the sale would help pay expenses for his sister, Terri, who suffers from multiple sclerosis, and some would go to the Muhammad Ali Foundation.Suggest a correction