But when the Cougars left the WAC to help form the Mountain West Conference in 1999, their series with the Miners ended abruptly. The two schools haven't met on the football field since 1998, when BYU defeated UTEP, 31-14.
The Cougars and Miners will renew their rivalry Saturday in the fifth annual New Mexico Bowl.
But was it ever a rivalry in the first place? BYU leads the all-time series, 28-7-1 and has won 25 of the last 27 meetings.
"I remember UTEP because my brother (Mat) played here at BYU, and certainly from the old WAC," said Cougar coach Bronco Mendenhall. "Most of our players have no idea about any of that former WAC affiliation, nor do I think it will play into the game whatsoever."
Some UTEP supporters, though, still consider BYU a big rival, even after all of these years.
"Longtime UTEP fans certainly remember. There's no question there's a sense of excitement here about this bowl game," said the Voice of the Miners, Jon Teicher. "The programs haven't played in 12 years. Still, for a segment for longtime UTEP fans they feel a little bit jilted by the schools that pulled out of the Western Athletic Conference to form the Mountain West in the late '90s. And BYU obviously was always the benchmark of the old WAC. Everybody was aiming at them. UTEP was no different. Those sentiments still exist today, even though they haven't played in a dozen years and haven't been in the same conference for that long. BYU's still one of the magical names in college football, being a former national champion and the excellence that LaVell Edwards' programs traditionally had. And since his retirement, BYU is still one of the standards of the college game."
Of course, there are many fans that have few or no memories of BYU-UTEP games.
"Sure, UTEP has developed fans since the breakup of the WAC that have no idea of what was once," Teicher said. "I think what's going to be odd about the game is, the players and most of the coaches on both sides have no idea (about the history). They weren't a part of it. It's not going to be the same as it would have been had these two teams been playing all along. But if that were the case, they wouldn't be matched up in the New Mexico Bowl, would they?"
Legendary coach LaVell Edwards is looking forward to seeing BYU and UTEP play again.
"Those old WAC days were fun days. We had some pretty good games with them," he said. "We had some one-sided games and some real good games."
Edwards added that what makes it even better is his longtime friend, former Weber State coach Mike Price, is coaching the Miners now. "He was always one of my favorite people around here," Edwards said. "Mike was a lot of fun.. He's a good football coach and it'll be a good ball game."
The BYU-UTEP rivalry was much fiercer in basketball as the two teams frequently battled for the WAC title. Last January, the Cougars played the Miners in basketball for the first time in years and came away with a win in El Paso. On Dec. 23, UTEP will visit the Cougars at the Marriott Center. The hoops meeting a year ago, Teicher said, didn't produce the electric atmosphere he had been expecting.
"It was a little strange. It goes to show that so much time has passed and UTEP obviously has developed new fans," he said. "It was played at a strange time, in early January and our students weren't back yet. But it was a quiet game. Personally, I was very surprised. It goes to show that a lot of time has passed and new rivalries develop. It's not quite the same."
New Mexico Bowl
BYU (6-6) vs. UTEP (6-6)
Dec. 18, noon
Radio: 1160 AM, 102.7 FM