In the 1950s and 1960s Gaslini performed with his own quartet. He was the first Italian musician mentioned as a "new talent" in the "Down Beat" poll and the first Italian officially invited to a jazz festival in the USA (New Orleans 1976-77). He worked with leading American soloists, such as Anthony Braxton, Steve Lacy, Don Cherry, Roswell Rudd, Eddie Gomez, Max Roach, Nacci Alberto, but also with the Argentinian Gato Barbieri and Frenchman Jean-Luc Ponty. 