He completed his studies at the Liszt Ferenc Academy of Music in 1963 under Lajos Hernádi.
From 1962 to 1969 he was a coach at the State Opera House, and since then he has been exlusively occupied as a soloist for the National Philharmonic Agency. His repertory has a large scale of piano music including the standard pieces of the classical literature, many contemporary works and he is credited with a number of first performances.
Ádám Fellegi won a prize in the 1966 Liszt+Bartók International Piano Competition and in the same year, the prize offered by the master course led by Jörg Demus, Alfred Brendel and Paul Badura Skoda in Vienna. In 1967, he was also granted an award in the Taormina Music Festival.
In 1973, he was awarded the Arthur Rubinstein Prize at the Villa Lobos Competition in Rio de Janeiro. He visited several times the United States and Canada where he was Artist+in+Residence for a longer period at Brock University and York University, Ontario.
In the last 15 years he also gave concerts in Germany, Italy, Austria, Cuba, England, Russia, Poland and Netherlands. The Hungarian national label (Hungaroton) published several recordings with him, for example the CD album of the complete piano music by Zoltán Kodály.
In the last ten years he produced TV programmes, exploring a new fusion of music, image and explanation. Explanatory introduction and "initiation" has become a standard regularity during his recitals in Hungarian, but in German, English, French and Italian as well. His most recent achievement in Rome featured the complete series of Piano Sonatas by Ludwig van Beethoven with his own introductory explanations in Italian language. He gave several Master Classes in the United States (University of Colorado, Boulder), in Canada (Brock University, St. Catherines, York University, Toronto). He led the Master Courses Liszt+Bartók at Festival Estival (Paris), Bartók Kodály, (Mulhouse, Colmar), for international roups of music teachers. In Hungary he is a well known professor of postgraduates.
He was awarded the Hungarian state prize "Franz Liszt" in 1984, the distinction "Pro Urbe" by Budapest 1994.