The observed asymmetry in the interfacial adhesion between ZnO and Ag is studied using a first principles density functional approach. The interface formed when ZnO is deposited on Ag (111) is experimentally measured to be stronger than that formed when Ag is deposited on ZnO (0001) and this indicates a possible difference in bonding geometries. It is found that because the ZnO (0001) surface does not exhibit atoms which are onefold coordinated with the sub-surface layer this restricts the way Ag can bond to the surface whereas no such restriction exists, when ZnO is deposited on the Ag (111) surface. The study focuses on a particular Ag (111)/ZnO (0001) interface which has rotated epitaxy and by calculating the ideal work of separation it is found that an O-terminated interface which is onefold coordinated with an adjacent Zn layer is significantly stronger than the corresponding interface which is threefold coordinated with an adjacent Zn layer. This is consistent with the observations, since the onefold coordinated interface cannot form when Ag is deposited on to ZnO (0001). Additional calculations indicate that the stronger onefold coordinated interface can also separate leaving oxygen on the Ag surface provided that surface relaxation effects are suppressed.