Head of the Department of Theoretical Physics at the Sofia University Faculty of Physics (11.02.1992 - 28.04.1994 and 27.06.1995 – 14.10.2003).
Dean of the Faculty of Physics, University of Sofia (1983 - 1985)
Vice-Rector of the University of Sofia (1985 - 1987).
Member of the Faculty Council, Faculty of Physics, University of Sofia (1980 - 1989 and 1995 - 2010).
Member of the Academic Council, University of Sofia (1983 -1989 and 1995 - 2010).
Member of the Scientific Council, Joint Institute of Nuclear Research, Dubna, Russia (1993 - 2010).
Editor in Chief of Bulgarian Journal of Physics (1998 - 2010)
Bulgarian delegate to the CERN Council (1999 - 2000)
Full Member of the Bulgarian Academy of Sciences (2004 - 2010)
Fellow of the Institute of Physics, United Kingdom (2003 - 2010)
Bulgarian delegate at CCE-FU (2006 - 2010)
Up to his death he was Editor in Chief of the Bulgarian Journal of Physics
Prof. Matey Mateev was member of the editorial board of the Balkan Physics Letters
1997 – 2003 е председател на Комисията за сътрудничество на България с Обединения институти за ядрени изследвания (ОИЯИ) - Дубна към Агенцията за ядрено регулиране.
M. Mateev was assistant professor (1964 - 1971) and Associate professor (1981 - 1984) and full professor in theoretical physics (1984 - 2010) in Department of theoretical physics at the Sofia University Faculty of Physics.
He lectured in Quantum Mechanics, Quantum Field Theory, Elementary Particle Physics.
He worked in the Laboratory of Theoretical Physics at the Joint Institute of Nuclear Research, Dubna, USSR (1971 - 1980).
Prof. M.Mateev was Vice-President of the Committee of Science at the Council of Ministers of Bulgaria (1986 - 1989).
First Deputy Minister of Public Education (1990).
Minister of the Education and Science of Bulgaria (1990 - 1991).
Member of the Presidium of the Supreme Attestation Commission to the Council of Ministers of Bulgaria (2006).
Prof. M. Mateev was Member of the Executive Committee of the Union of Physicists in Bulgaria (1995 - 2001).
He was President of the Union of Physicists in Bulgaria (2001 - 2010).
He was Vice-president of the Balkan Physical Union (1997 - 2003).
М. Матеев, Предговор, Емил Наджаков, Физика електромагнитни и оптични явления, Университетска библиотека 424, серия Университетска класика, Университетско издателство, София (2004) с. 11-13
Ц. Соколова, Акад. Матей Матеев - ученият с мисия, Сега, 19.11.2005
Удар в дърво уби акад. Матей Матеев и съпругата му, Блиц, 26 юли 2010
При катастрофа загина академик Матей Матеев, Труд, 26 юли 2010