Rafael Ithier, is a former member of Rafael Cortijo's "Cortijo y su Combo" orchestra. After singer Ismael Rivera faced legal problems in Panama, some of the group's musicians departed, with Ithier relocating temporarily to the eastern United States, before returning to Puerto Rico.
Rafael Alvarez Guedes, the Cuban-born owner of the Gema recording label (and brother of comedic actor Guillermo), needed a backing band to record an album for legendary Dominican merengue singer Joseíto Mateo. He asked Ithier for assistance, and Ithier responded by bringing in many of his former colleagues to the studio. For their first recording sessions, the orchestra included some musicians from Cortijo's original lineup, including saxophonists Hector Santos and Eddie “La Bala” Perez, trumpet player Rogelio "Kito" Velez, and percussionists Martín Quiñones, Miguel Cruz and Roberto Roena. Alvarez Guedes was told by Ithier that the name of the group was El Gran Combo, as to refer to the musicians' former affiliation, but addressing their regrouping as a "new and improved" version of Cortijo's orchestra. The album they recorded was titled Menéame Los Mangos, El Gran Combo con Joseito Mateo (the phrase translates as Shake My Handles or Shake My Mangoes, a play on words).
The group met again to define the foundations of a proper orchestra and chose singers Daniel Vázquez, Pellín Rodríguez and Chiquitín García (who later composed, among other major EGC hits, "No Hago Más Ná", or "I Don't Do A Thing").
On May 21, 1962, El Gran Combo was heard for the first time on Puerto Rican radio. Later on, they became the in-studio musicians of the live television show, La Taberna India, sponsored by India Beer.
After their live debut at Hotel La Concha in San Juan, Puerto Rico, Chiquitín García left the orchestra. Vocalist Sammy Ayala, who had also played with Ithier in the Cortijo orchestra, recommended the hiring of Andy Montañez. Felipe Rodríguez, a legendary singer of romantic music, also followed the group's career closely, sometimes even making suggestions to Ithier.
On November 20, 1963, El Gran Combo released their first group album, Acángana, with Rodríguez and Montañez as lead singers. The album reached gold status and became a number one hit in New York, Panama and Puerto Rico. Their success opened doors for them in many Latin American markets and they gained an exclusivity spot on the Puerto Rican television show, El Show de las 12.
On 1964, trumpet player and arranger Elías Lopés joined the orchestra, coinciding with the group's first popularity wave. With their daily TV appearances and extensive touring, however, demand for the group declined due to overexposure. Still, in 1967, their album Boogaloo con el Gran Combo also reached gold status. In 1969, Roena and Lopés left the orchestra to form the Apollo Sound together. Despite all this, that same year the group was awarded an Agüeybana de Oro in Puerto Rico.
In 1970, their contract with Gema Records wasn't renewed. Despite offers from the renowned Motown label, El Gran Combo decided to produce their own albums, under the label Combo Records. Their first album under their label, EGC, is titled Estamos Primeros.