By 1980 the group had signed a contract with Discos CBS International, the Miami-based Hispanic division of CBS Records. Between 1981 and 1983 the Miami Sound Machine recorded four Spanish-language albums made up of ballads, disco, pop, and sambas. The Miami Sound Machine first met with success in Spanish-speaking countries. The group had dozens of hit songs around the worldvëparticularly in Venezuela, Peru, Panama, and Honduras—but enjoyed little recognition in the United States.

The Miami Sound Machine's first North American hit was from the band's first English album, Eyes of Innocence. The disco single "Dr. Beat" went to the top of the European dance charts. The song's popularity prompted CBS to move the group to Epic, a parent label, and inspired group members to write songs in English, first with a couple of numbers on the otherwise Spanish-language record Conga. The rousing dance number "Conga" itself became the first single to crack Billboard's pop, dance, black, and Latin charts simultaneously.