Complete 11I and 13C spectral assignments by 2D NMR means are presented for a new cyclodepsipeptide namely didemnin H, isolated from Trididemnum cyanophorum (Didemnidae).Didemnins are a class of depsipeptides isolated from Caribbean tunicates of the Didemnidae family showing antitumor1 and antiviral2 properties and a potent immunosuppressive activity3. Didemnin B, the most prominent member of this peptidic group, was first isolated by Rinehart and his coworkers in 19814, then later by Van der Helm5 and Fenical6 from Trididemnum solidum and by Guyot7 and us8 from Trididemnum cyanophorum (an ascidian living in symbiotic association with an unicellular alga - Cyanophyta -Synechocystis trididenmi )9. This family of cyclodepsipeptides has numerous members such as didemnins A, C D. E and nordidemnins 4.10. More recently, continued examination provided three new congeners fromTrididemnum solidum : didemnins G, X, Y^{11,12} and, from Aplydium albicans (Polyclinidae), a Mediterranean tunicate, dehydrodidemnin B^{13} , I4 . The structural elucidation of most of these compounds was mainly based on HRFAB mass spectrometry. We report here the structural elucidation of didemnin H and the complete 1H and 13C NMR spectral assignments by means of a combination of mass spectrometry and one and two-dimensional NMR experiments.