In 1981 Llerenas won the prestigious international prize, the Rolex Award for Enterprise, for his research and documentation of Mexican traditional music and two years later the three friends released the 'Antología del Son de México', a boxed set of six long play records that represented a sample of the recordings that they had made.

In 1976, motivated by their recordings of Mexican music, the three men began to travel to the Caribbean. The first countries that they visited were the Dominican Republic, Haití, Panamá, Belize, Costa Rica, Saint Kitts, Martinica, Guadalupe and Antigua. In 1985 Llerenas went to Cuba for the first time and, more than 15 years later, he continues to visit the island several times a year to record different styles of traditional music, especially Cuban son and bolero.