MATT-160 (1962) is available in pdf format.
Asymptotology
Author: Martin D. Kruskal
Abstract: Asymptotics is the science which deals with such questions as the asymptotic evaluation of integrals, of solutions of differential equations, etc., in various limiting cases. Elements of this science may be learned from the works of van der Corput, Erdelyi, and de Bruijn, and advanced aspects from the numerous references in Friedrich's cited article. By asymptotology, I mean something much broader than asymptotics, but including it; pending further elaboration, I would briefly define asymptotology as the art of dealing with applied mathematical systems in limiting cases.