 From 1964 to 1969, he served as an Assistant, Docent, Professor at the Faculty of Law of the Tbilisi State University; from 1969 to 1970, he was the Head of the Department of International Law.From 1970 to 1977, Aleksidze was Senior Officer at the Department of Human Rights of the United Nations Secretariat (New York, Geneva); from 1970 to 1975, he was Secretary of the Sub-Commission on Prevention of Discrimination and Protection of Minorities; from 1975 to 1977, he was Head of the Department of Consultancy Service and Special Tasks; Personal Representative of the UN Secretary General and an organizer at the inter-state seminars arranged by the section.Since 1970, Aleksidze delivered lectures on the persisting problems of international law at famous scientific and educational institutions, including the Emory and Boston Universities (the United States); the Humboldt University (Germany); the Hague Academy of International Law; the State Universities of Kiev, Azerbaijan and Armenia; the Academy of Human Rights (Greece); and the State University of Latvia.