Le­vych worked as a book designer and illustrator of children’s books for the Veselka publishing house, and served as chief art editor of the magazine Malyatko. He created illustrations for children’s stories by Hryhir Tiutiunnyk.
Le­vych was one of the leading figures of the Ukrainian art underground of the late 1960s – early 1980s. Like many of the Sixtiers generation, he sought to revive not only artistic techniques but also the very “language” of art suppressed under the doctrine of socialist realism.
His work is characterized by a distinctive authorial style and metaphorical imagery. His art, that was far removed from the themes of socialist realism, defined his unofficial status: his works were not exhibited publicly for fifteen years (from 1970 to 1985).
Today, his works are preserved in the National Art Museum of Ukraine, the Museum of the History of Kyiv, regional art museums across Ukraine, the Zimmerli Art Museum at Rutgers University (New Jersey, USA), as well as in private collections in Ukraine, Russia, Bulgaria, the USA, the United Kingdom, Israel, Germany.