In analogy to the technology balance of payments, in this paper we propose a possible way to set up a "balance of knowledge flows" (BKF), recording world flows of knowledge within the scientific community. Adopting a pure bibliometric approach, the "knowledge" traced in the BKF is that produced and exchanged by the scientific community by means of publications and relevant citations. A description of the theoretical foundation of such a tool is presented together with its empirical testing over the scientific production of four different countries. The BKF can be part of yearly reports of science and technology indicators, aimed at informing research policy.