Cognitive researches on the polysemy of prepositions have all along focused on the motivation of meaning extensions andignored the effect of contextual enrichment ,which causes rampant polysemy , as shownin thecaseof OVER .Basedon the Dynamic Construal Approach to Meaning advanced by Croft & Cruse ,a Double-Layer Network Model of Polysemy is set on OVER , with the concept upper layer and the context lower layer in it . The upper layer contains one major category and two minor ones , representing ,respectively ,(1) ABOVE(MOBILE OR NOT) , (2) ON THE OTHER SIDE OF ,and (3) COVERING . They all have their prototypes . The upper layer shows Lakoff's radial network representation and the lower layer shows Rosch's earlier standard version of overlapping sets representation .The upper layer'sinterrelated prototy picalcatego riesarep sychologicalentities denoted by the lexeme and constitute the source of contextual extensions .The lower layer's meaning extensions are the results of online interpretation of the prototypical categories in light of cognitive context and with different construals . The model is characteristic of contextual flexibility and openness .