This paper makes use of the tools available in Cognitive Linguistics in order to present an analysis of the image-schematic component of certain metaphorical expressions. Specifically, the author focuses on how metaphors based on the CONTAINER and PATH image-schemas are constructed and processed. In order to achieve this purpose, the author analyses these expressions under the light of the 'many-space' model (Turner and Fauconnier 1994, 1996) and a reformulation of the Invariance Principle provided by Ruiz de Mendoza (1997a). The notion of schematic enrichment also proves to be useful in the sense that it is compatible with the basics of the many-space model, and it also accounts for the establishment of hierarchies of prominence among image-schemas. (Noelia Jiménez Martínez-Losa and Francisco Ruiz de Mendoza)