After attending art school in Prague for four years (1952–56), Nešleha studied at the Academy of Arts, Architecture and Design in Prague in the studio of monumental and applied painting headed by Professor Alois Fišárek (1956–62). His diploma work, an abstract painting that he had designed for the Concert Hall in Hradec Králové, was banned and destroyed because it was judged ideologically objectionable by the communist state. To complete his degree, Nešleha then used a collection of expressionist paintings that he had made in the course of his studies; he received a school prize for this work. In 1960 he joined a group of avant-garde artists in Prague called "Confrontations I and II". Through the activities of this group, he met graphic artist Vladimír Boudník and became friends with theoreticians František Šmejkal and Jan Kříž. His career was interrupted for two years by compulsory military service (1962–64). In 1966 he became involved in the activities of theoretician and art critic Jindřich Chalupecký. In the spring of 1968 the French Government awarded him a scholarship to spend three months in Paris; he took this opportunity to visit various museums and monuments in France. He married Mahulena Hromádkova (now , an art historian) later that year; their daughter Johanna G. Nešlehová, a statistician, was born in 1977.
