The breeds were recently recognized by the American Kennel Club, the governing body of U.S. dog shows, said Brandi Hunter, the vice president of public relations and communications for the AKC.
"These breeds are beautiful, unique and have met the requirements to be fully recognized by the AKC," she told ABC News.
These breeds were recognized by the AKC in 2016, making them eligible to compete in this year's Westminster Dog Show and all other AKC sanctioned events, Hunter said.
According to the AKC's website, the sloughi is a "reserved" and "graceful" breed that originated in North Africa and was used to hunt game; the American hairless terrier is "energetic, alert, curious and intelligent"; and the pumi is a Hungarian breed, adept at keeping livestock under control.
The 2017 Westminster Dog Show begins Saturday, Feb. 11.