The family first lived in the United States before returning to Europe and settling in the Netherlands.

Marek then taught at the University of South Carolina before returning to Sheffield in 1981 as a Research Fellow, later holding the positions of Lecturer, Senior Lecturer, Reader and finally Professor of European Prehistory.

Overall he spent thirty years at Sheffield, with spells as a visiting professor at several institutions across Europe and North America.

[1][2] Zvelebil's primary research interest was in the European Mesolithic and Mesolithic-Neolithic transition, particularly in the Baltic region.

With the dissolution of the Soviet Union in 1991, Zvelebil was able to extend his research, looking at early farming cultures in eastern Europe and Siberian hunter-gatherer peoples.