János Kulka studied conducting at the Music Academy under János Ferencsik and László Somogyi between 1947 and 1951. He also studied piano, contra-bass and percussion, as well as completing the course in composition as János Viski's student (1945/46-1950/51), and visiting the classes of Kodály and Leo Weiner. He intended to become an opera and symphonic conductor, but also performed as a pianist.
Kulka began his career at the Opera as a couch, and then became a conductor and chorus master. In 1957 he emigrated to Vienna; it was from here that Ferenc Fricsay invited him to Münnich, to the Bavarian State Opera. From here onwards Kulka's career trajectory rose in Germany. In 1959 he became chief conductor of the Württemberg Opera in Stuttgart, and two years later of the Hamburg Opera. From 1964 onwards he was music director in Wuppertal, in 1975 went to Stuttgart again as chief conductor. Between 1976 and 1987 he was the chief conductor of the Norwestdeutsche Philharmonie. He appeared as guest conductor in many countries, among others in the Vienna, Brussels, Zürich, Boston, Buenos Aires and Budapest opera houses. Besides the classic opera compositions, there is a significant weight of contemporary composers (among others Stravinsky, Penderecki, Janacek, Dallapiccola, Schönberg, Petrovics, Szokolay) in his repertoire. He conducted a number of original premieres (Boris Blacher: Yvonne, Prinzessin von Burgund, 1973; Giselher Klebe: Jacobovsky unde der Oberst, 1982; Konrad Boehmer: Doktor Faustus, 1985).
He made many recordings, among them Chopin's F minor piano concerto with Tamás Vásáry and the Berlin Philharmonic, as well as selections from operas with such singers as Grace Bumbry, Walter Berry, Brigitte Fassbaender and Teresa Stratas, and a full recording of Verdi's Troubadour.
He conducted on numerous occasions in Hungary as well, first as an opera conductor, then, on the second occasion – in 1969 – at a concert. The following is what a critic wrote of this concert: "János Kulka's personality, both disciplined and capable of disciplining, manifested itself to advantage in the Rachmaninov piano concerto. As our contemporary musical-aesthetic thinking is moving away from this overflowing late romantic world, the performer's responsibility increases. (…) Owing to his very fine sense of style, Kulka manages to sift out of the work the bombastic elements, to discipline the Rachmaninovian sentiments, keeping them elegant and sincere. (…) On the basis of this concert, János Kulka comes across as an excellent conductor, with safe hands, capable of a virtuosic conducting performance and demonstrating a very fine sense of style." At a 1986 concert he conducted, among other things, Brahms' Double Concerto, with Dénes Kovács and Miklós Perényi, and with the State Concert Orchestra. A critic wrote: "In working out the orchestral accompaniment, I would regard Kulka's chief virtue to lie in the sure style with which he showed up first of all the strong, definite basic character of the work: with marked melodic and rhythmic phrasing, strong emphases…".
János Kulka died on 19th October, 2001, in Stuttgart.