To solve this problem, we need to understand the differences between archaebacteria and eubacteria.$\newline$Archaebacteria and eubacteria are both prokaryotes, but they have several key differences:$\newline$• Archaebacteria have unique cell membrane structures that differ significantly from those of eubacteria.$\newline$• The cell membranes of archaebacteria contain ether linkages in their phospholipids,$\newline$ whereas eubacteria typically have ester linkages.$\newline$• This structural difference in the cell membrane is crucial for the survival of archaebacteria in extreme environments.$\newline$• Other differences include variations in ribosomal RNA sequences and the presence of different cell wall components.$\newline$Analyzing the options:$\newline$• Option 1: Cell membrane structure - This is correct as archaebacteria have distinct cell membrane structures.$\newline$• Option 2: Mode of nutrition - Both groups can have similar modes of nutrition, such as autotrophy or heterotrophy.$\newline$• Option 3: Cell shape - Both archaebacteria and eubacteria can have similar shapes, such as cocci or bacilli.$\newline$• Option 4: Mode of reproduction - Both reproduce asexually, primarily through binary fission.$\newline$Therefore, the correct option is Option 1.