The International Conference "Foundations of Software Science and Compu- tion Structures" (FOSSACS) is a constituent of the "Joint European Conferences on Theoryand Practice of Software" (ETAPS). The present volume contains the contributions to FOSSACS'99, the second conference in this series, which took place in Amsterdam. As formulated in the call for papers, FOSSACS focusses on "papers which o?er progress in foundational research with a clear signi?cance for software science. A central issue is theories and methods which support the speci?cation, tra- formation, veri?cation, and analysis of programs and software systems." The articles in this volume represent a wide spectrum of approaches to this general aim. In manypapers, one ?nds the studyof new concepts and methods which are motivated byrecent trends (or problems) in the practical use of software and information technology. The volume contains 18 contributed papers, preceded bythree invited papers. The ?rst, byM. Abadi, accompanies his "unifying invited lecture" addressed to the whole ETAPS audience. The second, byJ. Esparza and J. Knoop, contains an application of the results presented byJ. Esparza in his invited lecture to FOSSACS'99. The third summarizes an invited tutorial byD. Sangiorgi p- sented to ETAPS'99.