Governments around the world seek for strategies to overcome the reliance on fossil resources and provide solutions for the most challenging contemporary global issues: food shortage, depletion of natural resources, environmental degradation and climate change. A very recent and widely diffused proposition is to transform economic systems into bio-based economies, which are based on new ways of intelligent and efficient use of biological resources and processes. If taken seriously, such endeavour calls for the creation and diffusion of new knowledge as basis for innovation and behavioural change on various levels and therefore often is referred to as knowledge-based bioeconomy. In the current debate, the requirement for innovation is mostly seen in the advance of the biotechnology sector. However, in order to fulfil the requirement of sustainability, which implicitly is connected with the bio-based economy, the transformation towards a bioeconomy requires a fundamental socio-economic transition and must comprise changes in technology as well as in markets, user practices, policy, culture and institutions. To illustrate a nation's capability for this transition, we refer to the concept of national innovation systems in its broad approach. With the help of an indicator-based multivariate analysis we detect similarities and dissimilarities of different national systems within the European Union as basis for a transition towards a knowledge-based bioeconomy. The analysis allows to compare the different strategies and to identify bottlenecks as well as success factors and promising approaches in order to design policy instruments to foster this imperative transformation.