There's a slight misconception in the question. Archaebacteria is an outdated term. The current classification system recognizes Archaea as a separate domain of life, alongside Bacteria and Eukarya.

Here's what all organisms in the domain Archaea have in common:

* Unique Cell Walls: They lack peptidoglycan, the structural component found in bacterial cell walls. Instead, they have unique cell wall compositions, often with pseudopeptidoglycans.

* Distinct Membrane Lipids: Archaea possess unique lipid structures in their cell membranes, different from both bacteria and eukaryotes.

* Unusual Gene Expression Mechanisms: Their mechanisms for transcribing DNA into RNA and translating RNA into proteins differ from those in bacteria and eukaryotes.

* Extremophile Adaptations: Many archaea thrive in extreme environments, such as hot springs, highly saline environments, and acidic or alkaline conditions. This includes:

* Thermophiles: Live in extremely hot environments

* Halophiles: Live in extremely salty environments

* Acidophiles: Live in highly acidic environments

* Alkalophiles: Live in highly alkaline environments

* Metabolic Diversity: Archaea exhibit a wide range of metabolic pathways, including methanogenesis (producing methane), sulfur reduction, and nitrogen fixation.

It's important to note that while they share these common characteristics, Archaea are a diverse group with a wide range of specific adaptations and metabolic strategies.