Concepts for sustainable bioeconomy systems are gradually replacing the ones on linear product chains. The reason is that continuously expanding linear chain activities are considered to contribute to climate change, reduced biodiversity, over-exploitation of resources, food insecurity, and the double burden of disease. Are sustainable bioeconomy systems a guarantee for a healthy planet? If yes, why, when, and how? In literature, different sustainability indicators have been presented to shed light on this complicated question. Due to high degrees of complexity and (...) interactions of actors in bioeconomy systems, trade-offs and non-linear outcomes became apparent. This fueled the debates about the normative dimensions of the bioeconomy. In particular, the behavior of actors and the utilization of products do not seem to be harmonized according to the environmental, social, and economic pillars of sustainability. Potential conflicts require a new conceptual framework that is here introduced. It consists of a ‘sustainability’ cylinder captured between an inner-cylinder, representing order, and an outer-cylinder for chaos, based on the laws of physics and complex adaptive systems. Such a framework permits (bioeconomy) systems to propagate in the sustainability zone only if they follow helical pathways serving as the new norms. Helices are a combination of two sinusoidal patterns. The first represents here the sustainable behavior of interacting actors and the second the balanced usage of resources and products. The latter counteracts current growth discourses. The applicability of the conceptual cylinder framework is positively verified via 9 cases in Europe, which encompass social-organizational and product-technological innovations. –. (shrink)