Cognitive linguistic research suggests that Slavic verbal prefix semantics may be profitably described by assuming a spatial prototype, and that non-spatial (abstract) prefixes derive metaphorically from this prototype. This dissertation uses a cognitive linguistic framework to establish a concise, systematic description of prototypes for prefixes and prepositions in Russian and Czech, and evaluates the nature of the relationship among the various senses of prefixes. The research presented here is aimed at carefully establishing the spatial meaning of prefixes. The primary motive for this research, however, is to evaluate the nature of the relation between spatial uses and abstract uses and to determine if abstract uses do indeed involve primarily spatial metaphor. A significant portion of the dissertation, therefore, is devoted to a discussion of the connection between spatial and abstract prefixation. A secondary purpose is to compare the spatial and abstract uses of prefixes in Czech and Russian, and to see whether differences in the verbal systems of these two languages can be correlated with underlying semantic differences at the spatial level.