Abstract: The nucleus of dinoflagellates had been used as the model of the primitive nucleus.However,this model was found unsuitable.According to this model the chromosomal basic protein of dinoflagellates should represent a very primitive nucleosomal histone-related protein and the differentiation of four nucleosomal histones should take place after the emergence of the primitive nucleus.But both two deductions were found to be incorrect.In other respect,various studies of molecular evloution studies showed dinoflagellates were not the most primitive ones among present-existing eukaryotes,but might only be the primitive ones among matakaryotes.Superkingdom Archezoa seems to be the primitive eukaryotes,which possess no mitochondria,no typical Golgi apparatus,and no 80S type of ribosomes,but have 70S type of ribosomes just as prokaryotes have.According to the studies of molecular evolution of large rRNAs and 5.8S rRNA,diplomonads,in turn,seem to be the most primitive ones among the present-existing Archezoa,therefore,their nucleus might perhaps be the suitable model of the primitive cell nucleus.Giardia lamblia was used as the representative of diplomonads and the nucleus of its trophozoite was studied in our laboratory in recent years,The following points were found:1.No nucleolus was found with various detection methods.2.The nuclear enevelope of Giardia was found incomplete for the first time.Large openings were seen in its nuclear envelope.The natural existence of the nuclear envelope openings has been confirmed by sequential ultrathin sectiontions.3.Nuclear matrix was already found in its nucleus.4.The nuclear.lamina seems very primitive because only lamin B was found it and it could not bear routine sequential specific extractions for demonstrating nuclear lamina and nuclear matrix.5.The centromere protein B and kinetochore porteins of Giardia were found mostly simlar to the corresponding proteins in various archaebacteria.6.Giardia nucleus was found already having five species of histones.7.Our preliminary observations showed that spindle and spindle microtubules have not been found within the dividing nucleus of Giardia.The possibility that the above described special characteristics were produced only due to the parasitic life of Giardia,was analyzed and refuted.ln literature,nucleolus was never found in several other genera of diplomonads,and in other genera heterochromatin structures were mistaken for nucleolus.According to the electron-microscopical photographs in literatue we found that nuclear envelope openings not only existed in Giardia,but also existed in other diplomonads,whether parasitic or free-living.The discovery of nuclear evelope openings in diplomonads confirmed our hypothesis on the origin of nuclear envelope from the primitvie endoplasmic reticulum in the prokaryotic acestor of eukaryotic cells (Li jing-yan,1979).In the light of the nucleus of diplomonads,we presumed that the primitive nucleus in evloutionary history should have nuclear matrix,nucleosomes,from species of nucleosomal histones and typical eukaryotic chromatin already,but still have no nucleolus and its nuclear envelope should be incomplete.Furthermore,we analyzed the facts concerned and proposed an inference about the archaebacterial ancestor of eukaryotic cells.The whole process of the evloutionary formation of cell nucleus was investigated,especially the formation of eukaryotic chromatin.The significance of the emergence of nuclear matrix in the formation of eukaryotic chromatin was emphasized.At the same time our hypothesis on the origin of nuclear envelope was also further developed.