MONTREAL — Irwin Shlafman , the owner of Fairmount Bagel, boasts that his bagels were the first in outer space, when his astronaut cousin brought them to the International Space Station.

He also says Fairmount, founded in 1919, is the oldest bagel joint in town.

Just don’t tell that to his arch-bagel-rival, Joe Morena, the jovial owner of nearby St-Viateur Bagel. He contends that his bagel place, opened in 1957, is Montreal’s longest continuously running bagel outfit, since Fairmount was closed for a time.

“His bagels went to the moon, yeah, sure,” Mr. Morena said. “But the oldest? Give me one iota of proof!”

The two men are competitors in the business of Montreal bagels, which have a distinctive flavor from being boiled in honey-infused water before being baked in a wood-burning oven.