Eukaryotic cells. Cells with nucleus and membrane bound organelles are eukaryotic. Eukaryotic means true nucleus, which means that their DNA is covered by the nuclear membrane and other organelles are covered with similar membranes.Cells without a nucleus and membrane-bound organelles would be called prokaryotes.ukaryotic means true nucleus, which means that their DNA is covered by the nuclear membrane and other organelles are covered with similar membranes. Cells without a nucleus and membrane-bound organelles would be called prokaryotes.