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In this paper we develop a model which represents the addressing of resources by processes executing on a virtual machine. The model distinguishes two maps: the ø-map which represents the map visible to the operating system software running on the virtual machine, and the f-map which is invisible to that software but which is manipulated by the virtual machine monitor running on the real machine. The ø-map maps process names into resource names and the f-map maps virtual resource names into real resource names. Thus, a process running on a virtual machine addresses its resources under the composed map f o ø. In recursive operation, f maps from one virtual machine level to another and we have f o f o ... o f o ø. The model is used to describe and characterize previous virtual machine designs. We also introduce and illustrate a general approach for implementing virtual machines which follows directly from the model. This design, the Hardware Virtualizer, handles all process exceptions directly within the executing virtual machine without software intervention. All resource faults (VM-faults) generated by a virtual machine are directed to the appropriate virtual machine monitor without the knowledge of processes on the virtual machine (regardless of the level of recursion).