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The Second International Conference on Unconventional Models of Compu- UMC'2K, organized by the Centre for Discrete Mathematics and The- tation, oretical Computer Science, the International Solvay Institutes for Physics and Chemistry and the Vrije Universiteit Brussel Theoretical Physics Division was held at Solvay Institutes from 13 to 16 December, 2000. The computers as we know them today, based on silicon chips, are get- ting better and better, cheaper and cheaper, and are doing more and more for us. Nonetheless, they still give rise to frustrations because they are unable to cope with many tasks of practical interest: Too many problems are effectively intractable. A simple example: cyber movie networks face the near impossible task of building a brand in a computing and communication almost vacuum. Fortunately, for billions of years nature itself has been "computing" with molecules and cells. These natural processes form the main motivation for the construction of radically new models of computation, the core interest of our conference. The ten invited speakers at the conference were: 1. Accardi (Rome, Italy), S. Bozapalidis (Thessaloniki, Greece), K. Gustafson (Boulder, USA), T. Head (Binghamton, USA), T. Hida (Nagoya, Japan), v. Ivanov (Dubna, Russia), G. Piiun (Bucharest, Romania), G. Rozenberg (Lei den, the Netherlands). H. Siegelmann (Haifa, Israel), and E. Winfree (Caltech, USA). The Programme Committee consisting ofM. Amos (Liverpool, UK), I. An- toniou (Co-chair, Brussels, Belgium), S. Bozapalidis (Thessaloniki, Greece), G.