The team in that time was formed by 14 players and within an era of double power, all played defensive and offensive roles and they were made hold the action of the match until someone was hurt.

In 1970, the Coach Gustavo Zavaleta re-baptized the team with the nickname "Borregos Salvajes" (Wild Rams) in order to identify it with this species, which is characterized by its constant fight to survive in highly risky situations, always dominating from the heights the atmosphere that surrounds it and showing its superiority before the others.

The Borregos Salvajes were crowned Champions of the Greater League of National Student Organization of American Football (ONEFA) on four occasions: 1971, 1972, 1974 and 1976.

But twelve years later, the American Football team of the ITESM returned to the league this time commanded by the Head Coach Frank González, after obtaining three championships in a row in the National Conference of ONEFA.

In 1992 the squad improved their record (8–1) and although they had a bad performance when losing to the Aguilas Blancas, won the privilege of being considered the best team in Mexico.

In 1994, before the expectation of and a doubt of others, one stays in the top and it obtained the second championship, this time against the Aztecas of the University of the Américas playing as a visitor and winning by a score of 17–10.

In 1996 at the Estadio Tecnológico de Monterrey crowded at its maximum capacity, the Borregos again reached the final game with the Aztecs of the UDLAP.

In 1998 it earned the championship, defeating the Aztecs of the UDLAP by a score of 20–17 at the Estadio Tecnológico de Monterrey crowded with 33,155 fans, in a game at noon on Saturday.

In 1999, the Borregos Salvajes obtained a second championship when defeating again the Aztecs of the UDLA by score of 38–25, this time the game was celebrated on the field nicknamed the Temple of the Pain in Cholula, Puebla.

In the 2002 season, the Borregos Salvajes arrived again at the final game a second consecutive year with the team directed by the Coach Frank González.

Nevertheless, in the third and fourth quarters, the Rams scored touchdowns to win another championship, as the team took 22 games without a defeat and 12 years without a loss to the Tigres.