Somogyi received his musical training under Zoltán Kodály and Leo Weiner at the Ferenc Liszt Academy at Budapest, where he was later to become leading professor of the Conductor's Class. While in Hungary he founded and led the Symphonia Orchestra, was Chief Conductor of the Hungarian Broadcasting, and guested with the Hungarian State Opera. He also conducted the most important orchestras in Poland, East Germany, Rumania, Yugoslavia and Bulgaria.
In 1956 he left his native country and was since active all over the world, including South America. His American debut in March 1961 with the Houston Symphony was a great success. From 1964 to 1968 he served as Chief Conductor of the Rochester Philharmonic Orchestra.