Peak during 1978-1990

In 1978, he signed a contract for CBS International, adding English, French, Portuguese, German and Italian to his language repertoire. Iglesias released the album De Nina a Mujer in 1981, from which he had his first hit in the English market with a Spanish cover of Begin the Beguine (a No.1 hit in the United Kingdom). He also released a collection, Julio, in 1983 building his reputation.

In 1984, he released the smash hit album 1100 Bel Air Place, which gave him considerable fame in English-language markets. The album sold three million albums in the US alone, with the first single To All The Girls I've Loved Before, a duet with Willie Nelson, reaching the top five on the Billboard Hot 100. The album also featured All of You, a hit duet with Diana Ross.

In 1985, his father was kidnapped but found well and alive after two agonizing weeks. This prompted Julio (divorced from Preysler), to move his family to Miami, Florida, where they settled in a mansion on Miami Beach. That year he also recorded duets with Diana Ross and Willie Nelson. It was rumored in 1986 that Julio, perhaps seeking to get away from all the fame and hoopla for one week, was found walking around the streets of Cayey, Puerto Rico, after disappearing for seven days. After visiting the island of the Dominican Republic he fell so in love with it that in late 2005 he adopted legally Dominican citizenship.

Iglesias won a Grammy Award for Best Latin Pop Album in the 1988 Grammy Awards for the album Un Hombre Solo (A Man Alone). He also recorded a duet with Stevie Wonder on My Love from his Non Stop album which achieved crossover success in 1988.

Stories of Julio's expensive private jets, boats, and houses became legendary during that decade, and his world tours took him to many countries and continents around the world performing in many sold out concerts among the vast female populations.