Trends of stagnation in highly developed innovative systems are actively debated nowadays. The paper analyses the important role played by fundamental research in preventing such a negative scenario. It explains the essence of the so-called ‘European paradox’, whereby Europe, despite a higher scientific potential than the US, is much less efficient in innovation. Evidence from Austria shows the current system of fundamental research has several drawbacks. These weaknesses could prevent it from being a driver of breakthrough innovations. One problem is the contradictions in career development mechanisms in academia and the lack of accumulated research competencies in the form of large academic entities that are funded on an ongoing basis. Compared with other countries, Austria has little attraction for highly qualified specialists and, respectively, for the dynamic high-tech sectors. In order to remedy the situation, it is recommended to particularly develop projects that aim to find answers to the ‘grand challenges’, in parallel to curiosity-driven research. In addition, we recommend creating organizations with sufficient administrative capacities and autonomy to attract qualified staff and funding with a view to implementing innovation over a long term horizon (10-20 years).