Companies and R&D institutions increasingly collaborate not only in isolated projects but also in knowledge-based networks. In those networks, participants combine expertise and applied problems to generate both 'problem-solving knowledge' and specialized knowledge: during the process of common problem-solving each partner acquires some of the specialized knowledge of the other partners as well as the newly generated problem-solving knowledge. This article examines the basic principles involved and provides a simple mathematical description of the step-by-step accumulation of knowledge through the solving of applied problems in a knowledge-based network. The rate of increase of the total amount of available knowledge in the network is derived and implications for the orientation of R&D institutes and companies are set out.