They formed the company Promociones Mora y Asociados (later Lucha Libre Internacional (LLI)), which would later become widely known as the Universal Wrestling Association (UWA), the name of its fictional governing body which was adopted from the short-lived American-based UWA promotion ran by Lou Thesz, and held their first show on January 29, 1975, creating the first true rival for EMLL in decades.

This working relationship resulted in a larger influx of foreign wrestlers than EMLL was ever able to produce and also led to the UWA actually gaining exclusive rights to promote a WWF branded championship, the WWF World Light Heavyweight Championship in the early 1980s, even if the promotion does not acknowledge this lineage in their official title history today.

By the early 1990s UWA began to struggle financially as several of their top wrestlers left the company to work for EMLL who could offer them more money.

[6] The UWA is remembered as the place where a lot of the main event wrestlers of the 1980s and 1990s for both CMLL and AAA got their starts, including El Canek, now considered a legend in lucha libre.

Some UWA titles are still being used today, some in Japanese promotions who bought the rights to the belts and the name to give them a lucha libre link, others are considered more "vanity" championships, personally owned by whoever holds them and are often used more as a storyline prop, although they are at times defended and even change hands.