His father was from Bessarabia. After Caspi's military service, The Three Fat Men became the They Don't Care trio. In the Yom Kippur War he toured army bases along with Leonard Cohen, who arranged his 1974 song "Lover Lover Lover" with Caspi. During the 70s he worked closely with Ehud Manor, another Israeli songwriter, and released some of his most popular songs: Lo Yadati SheTelchi Mimeni (I Didn't Know You Would Leave Me), Brit Olam (Covenant of Love), and Shir HaYonah (The Song of the Dove). Over the next few decades, Caspi had a prolific musical career, released dozens of records and collaborated with some of the biggest and most well known Israeli artists of the time: Shlomo Gronich, Ehud Manor, Yehudit Ravitz, and Shalom Hanoch. He has released several more albums, of which the latest is Like in a Dance, released in 2017. Caspi has released close to 1,000 songs, both remakes of ol- der songs and his original creations. His musical style is well known, especially for his harmony and popular writing style. With some Israeli artists (chiefly Riki Gal), he not only took on the role of composer, but also of the producer. For Riki's 1996 album I Love You More, he took responsibility for complete production and also songwriting. At least once, at the 1976 Eurovision Song Contest, he also served as a conductor, lea- ding the Netherlands' prestigious Metropole Orkest in his composition "Emor Shalom", performed by Chocolate, Menta, Mastik and also arranged by Caspi.