On March 8/9, 1976 a workshop on "Mathematical Models in Medicine" was held at Mainz (German Federal Republic) by the group of "Mathe- matical Models" of the Deutsche Gesellschaft fUr Medizinische Doku- mentation, Informatik und Statistik. Purpose of this conference was to bring together experts from the GFR and neighbouring countries working in this field to evaluate possibilities and limits of this area of research in discussions with interested participants. This issue of Lecture Notes contains the invited contributions as well as the relevan~ remarks made by the discussants. Corresponding to the aims of the workshop the contributors had been encouraged to demon- strate their mathematical models in the light of actual applied examples. It had been our intention to restrict attention to a small number of specific areas in order to achieve a concentrated in depth treatment in these restricted areas. The areas chosen contain two - Epidemio- logy and Cell Models - which in the organisers feeling are not yet as well established in Continental Europe and one - Pharmacokinetic- with a more direct appeal to applied workers. While in the Epidemio- logy of infectious and parasitic diseases today strategies of control and eradication are gaining importance, the cell models are concerned with explaining the modes of genesis of cancerous growth and the kinetics and interactions within multi-cell structures.