Avellanet achieved teen-idol status in Puerto Rico during the 1960s, as a member of the "Nueva Ola" pop music movement. Helped by Alfred D. Herger, he was a member of a group of teen sensations that included Lissette Alvarez (to whom Avellanet got married), Lucecita Benítez, Yolandita Monge, Ednita Nazario and Charlie Robles, among others. Such was his popularity that he was booked to do three shows on New Year's Eve 1961 and New Year's Day 1962. With "La Nueva Ola", he recorded his first album, titled "Fugitiva." His first hit was a Spanish version of Marty Robbins' "Devil Woman" loosely translated by Herger under the title "Magia Blanca" ("White Magic"). He later had his first major international hit with another song adapted to Spanish, a version of pop standard "I Can't Stop Loving You" titled "Jamás te olvidaré" ("I Will Never Forget You").