The problems of the origin of primary cells and eukaryotic cells are discussed in terms of possible role of interactions between nucleic acids with lipid membrane according to corresponding original hypothesis. We propose that there are two main hypotheses of the origin of primary cells: (a). RNA appeared before proteins and DNA [Nature 213 (1967) 119]; (b). it is needed for the appearance of a primary cell, the volume closed by the lipid membrane. There was no information about the ways on how RNA appeared inside that volume for saving the reaction products around. Our hypothesis suggests that one of the starting points in the origination of primary cells was the interaction of nucleic acid and lipid membrane bubbles in the presence of metal (II) ions (which existed in high concentrations in prebiotic conditions), and this resulted in the enclosing of the pro-RNAs inside the lipid membrane. This hypothesis is formulated by us on the basis of experimental biochemical and biophysical studies of the DNA/RNA-phospholipid vesicles interactions in the presence of metal ions (II) fulfilled in the Institute of Biomedical Chemistry, RAMS, Moscow and Institute of Biophysics, RAS, Pushchino. Our belief is that DNA-membrane contacts (DNA-MCs) played an important role in the prokaryotes-to-eukaryotes transition. The model of the confluence of four prokaryotic cells may explain the prokaryotes-to-eukaryotes transition by the way of eukaryotic nuclear pore formation from prokaryotic Bayer' contacts. The main requirement for the following fusion of prokaryotic cells must be their mutual orientation. After possible association, the division of the formed cell is begun. The great advantage of the model of four prokaryotic cells is the profit in the metabolism and the possibility of the intensive growth of intercellular membrane structures.