Blissfully unenlightened on the realities of American sports, Shrum declared then that the football squad would engage in the Rose Bowl game within a decade. The men’s soccer team did, indeed, win the 1976 N.A.I.A. championship — in the Rose Bowl stadium in Pasadena, Calif.

With its past membership in the National Association of Intercollegiate Athletics, its current affiliation with the Great Northwest Athletic Conference, a far-flung student body (18 percent come from outside Canada) and aspirations to lift its profile academically and athletically, Simon Fraser seemed a logical candidate to seek N.C.A.A. admission.

The transition was fraught with headaches, though, small and large. Coaches had to receive a crash course on the N.C.A.A.’s thick rules manual, which is “Atlas Shrugged” in length compared with its Canadian counterpart.

The men’s soccer coach, Alan Koch, who has worked at N.C.A.A. colleges, said he and other coaches at the university were accustomed to being permitted to call recruits as often as they liked. They had to start observing once-a-week phone contact, per N.C.A.A. regulations.

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Simon Fraser also needed accreditation from a United States agency before joining the N.C.A.A. Given the university’s good academic reputation, the process was modified to allow for it to conditionally join the organization in the meantime.

“People say how inflexible the N.C.A.A. is,” Richards said. “They were flexible with us.”

Still, Simon Fraser was disappointed this season when informed by the N.C.A.A. that it could not host early-round tournament games, a perk for being designated a top regional seed, because visiting players might encounter passport or visa problems on such short notice.

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“This is all new,” said Richards, who plans to consult Canadian authorities about dealing with those issues in future seasons. “There are growing pains.”

Simon Fraser’s unique circumstances provide an easy target for opposing fans. “They yell, ‘Go back home,’ “ striker Carlo Basso said. Fans chanted “U-S-A” throughout one road game.

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There has been no discernible reaction to the teams’ nickname, though. The term in Scotland, Simon Fraser’s ancestral land, is synonymous with family. In the United States, a slightly different spelling can cause discomfort. Koch said that when he was playing on the soccer team in the late 1990s, the team was identified over the public-address system at Legion Field in Birmingham, Ala., as the Clan. “Total silence,” he said.

The teams carry a sense of extra responsibility. “You are playing, in a sense, for your country,” said Basso, who is from Coquitlam, British Columbia.

Athletes belt out their national anthem before events. “I know the words better than the Swiss one,” the team’s Swiss defender Marco Voegeli said.

Both players said they had been attracted to Simon Fraser at least partly by its N.C.A.A. status. Another incentive, at least for those who wish to play professionally, is that Major League Soccer bars its teams from drafting players from the rosters of Canadian college association members.

As a result of its N.C.A.A. ties, Simon Fraser anticipates it will have greater geographic diversity on its teams, fueled partly by a pipeline from the United States. Americans who play for the Clan, or who compete against them, can experience the high altitude of sites that have become so shrouded in fog — hence the teams’ mascot, McFogg the Dog — that the action becomes invisible from certain vantage points.

They might also encounter the wildlife that wanders nearby, including bears, cougars and coyotes.

Soon, soccer’s Division II Final Four might gain even more international atmosphere. The N.C.A.A. is weighing a proposal in January that would permit universities in Mexico to apply, and two have expressed interest.