Abstract. In this paper there are presented and analyzed some {\em natural} differential structures on the space of smooth mappings. Naturality means that they are strongly related to the structures of spaces between which the smooth mappings considered are defined. This paper is a continuation of the investigations presented in \cite{Brno95} (where one can find the mathematical and the physical motivation).
AMSclassification. 54C35, 58A40, 58D15
Keywords. Function space, smooth mapping, differential structure, differential space