[1] From 1997 to 1999, he served as president of the Institut de Droit International[1] and served as vice president of The Hague Academy of International Law from 2004 to 2024.
[3][6][7] Jayme was member of the Institut de Droit International whose president he was from 1997 to 1999.
[1][3] From 2004 until his death, he was vice president of the Curatorium of The Hague Academy of International Law.
[1][3] He was honorary doctor of the universities of Ferrara (1991),[1][3][6] Budapest (2000),[1][3] Montpellier (2003),[1][3][6] Porto Alegre (UFRGS) (2003)[1][6] and Coimbra, Académicien titulaire of the Académie internationale de droit comparé (Paris).
[6][8] He was a member of the Heidelberg Academy for Sciences and Humanities (1989),[6][9] Istituto Veneto di Scienze, Lettere ed Arti (2004)[3] and a foreign member of the Royal Netherlands Academy of Arts and Sciences (2005).