Hybrid systems are interacting networks of digital and continuous systems. - brid systems arise throughout business and industry in areas such as interactive distributed simulation, trac control, plant process control, military command and control, aircraft and robot design, and path planning. Three of the fun- mental problems that hybrid systems theory should address are: How to model physical and information systems as hybrid systems; how to verify that their - havior satis es program or performance specic ations; and how to extract from performancespeci cationsforanetworkofphysicalsystemsandtheirsimulation models digital control programs which will force the network to obey its perf- mance speci cation. This rapidly developing area is at the interface of control, engineeringandcomputer science. Methods under developmentareextensionsof thosefromdiverseareassuchasprogramveri cation,concurrentanddistributed processes, logic programming, logics of programs, discrete event simulation, c- culus of variations, optimization, di erential geometry, Lie algebras, automata theory, dynamical systems, etc. When the rst LNCS volume Hybrid Systems was published in 1993, the e ect was to focus the attention of researchers worldwide on developing theory andengineeringtoolsapplicabletohybridsystemsinwhichcontinuousprocesses interact with digital programs in real time. At the time of publication of this fth volume, there is general agreement that this is an important area in which mathematics, control engineering, and computer science can be fruitfully c- bined. There are now hybrid system sections in many engineering and computer scienceinternationalmeetings,hybridsystems researchgroupsin manyuniver- ties and industrial laboratories,and also other excellent series of hybrid systems conferences.