The central problem of the origin and early evolution of the eukaryotic cell is the origin of the cell nucleus, because the cell nucleus, with its double-layered nuclear envelope, is the most prominent and important morphological mark distinguishing eukaryotic cells from prokaryotes. Eukaryotic cells may have no chloroplast, mitochondria or flagellum, but they must possess a cell nucleus.The cell nucleus itself is a very complicated structure. If we try to make clear the origin and early evolution of the cell nucleus, we ought to investigate the origin and evolution of each morphological component of a cell nucleus. My monograph on 'The genesis of eukaryotic cells in the evolutionary history of life '(1979, Science Press, Beijing, in Chinese)[1], mainly attempted to make some effort in this regard. However, to date, the hypothetical model of a fully depicted nucleus of a primitive cell has not been constructed. It seems likely that our recent studies of the nucleus of Giardia (diplomonad) have provided a realistic basis to construct such a model.