<p>The term sustainability has received much attention in many spheres: in scientific discourse, international negotiations, policy, marketing, business, media and elsewhere. While the use of the term sustainability has become almost inflationary in both science and society, the work on theories of sustainability has received much less attention. This paper provides theoretical work on sustainability. Thereby it uses a non-anthropocentric approach. Based on accepted knowledge from natural sciences five processes are identified that conceptualize sustainability. Building on this, a necessary and sufficient condition is developed as theorems for sustainability. A proposition lays the foundation for identifying possible threats to sustainability. The paper then discusses sustainability and marketing with two further propositions.</p>