Nuclear migration is a general term for the movement of the nucleus towards a specific site in the cell. These movements are involved in a number of fundamental biological processes, such as fertilization, cell division, and embryonic development. Despite of its importance, the mechanism of nuclear migration is still poorly understood in mammalian cells. In order to shed light on the mechanical processes underlying nuclear movements, we adapted a micro-patterning based assay. C6 rat and U87 human glioma cells seeded on fibronectin patterns--thereby forced into a bipolar morphology--displayed oscillatory movements of the nucleus or the whole cell, respectively. We found that both the actomyosin system and microtubules are involved in the nuclear/cellular movements of both cell lines, but their contributions are cell-/migration-type specific. Dynein activity was necessary for nuclear migration of C6 cells but active myosin-II was dispensable. On the other hand, coupled nuclear and cellular movements of U87 cells were driven by actomyosin contraction. We explain these cell-line dependent effects by the intrinsic differences in the overall mechanical tension due to the various cytoskeletal elements inside the cell. Our observations showed that the movements of the nucleus and the centrosome are strongly correlated and display large variation, indicating a tight but flexible coupling between them. The data also indicate that the forces responsible for nuclear movements are not acting directly via the centrosome. Based on our observations, we propose a new model for nuclear oscillations in C6 cells in which dynein and microtubule dynamics are the main drivers of nuclear movements. This mechanism is similar to the meiotic nuclear oscillations of Schizosaccharomyces pombe and may be evolutionary conserved.