Our interdisciplinary research group "Epistemic Systems" investigates the formation of scientific theories, viewed as a paradigmatic case of creative problem solving. 1 The basis of our analysis is a wide spectrum of historical cases: Stimulated by a publication of Herbert Simon, we analysed extensively the discovery of the urea cycle by Hans Krebs (Gral]hoff ) on the basis of his laboratory notebooks; we carried out several case studies taken from early 20th century physics (Grat]hoff ); and detailed technical commentary on Kepler’s discovery of planetary ellipse orbits is on the way (Gral]hoff, Neugebauer, forthcoming). For these case studies all available historical documents of specific discovery processes--laboratory notebooks, letters and publications--have been gathered and evaluated. By examining these case studies we show that methods of discovery exist in different scientific areas and different methodological situations. In all cases we can explain creative problem solving processes by methodological rules. The domain-specific methods vary; yet we see a (rather unexpected) common stock of methodological principles. It contains general heuristics for model formation and rules for generating and evaluating causal hypotheses. The identified methods of scientific discovery were consequently implemented as a cognitive model of discovery on a computer.