The messenger paradigm is an alternative to computer communication based on the exchange of programs called messengers which are afterwards executed, instead of messages that are interpreted. The communication by messenger paradigm can be used to implement both low level software such as communication protocols and high level software such as distributed applications. Using the messenger paradigm for computer communication requires that each host be "equipped" with a runtime environment called messenger platform that can execute messengers that reach the platform. MØ is one such platform. MOS is a distributed micro-kernel designed for the efficient execution of messengers and implemented on i386 machines; it contains a MØ platform. It supports the concurrent execution of messengers on a given node. Messengers running on the same node can exchange data through a common store. Messenger behavior is expressed in the MØ messenger language understood by all messenger platforms. MØ is an interpreted language. Messengers see the memory provided by a MOS as a set of dictionaries where information is stored as pairs consisting of a key and a value. The key is used to access the value associated to a given information. In this paper, we present a memory consistency model, called access consistency, that is well suited to implement a distributed shared memory to extend the common store available for messengers running on the same MOS node to spawn a network of MOS nodes; i.e. to allow messengers to share information irrespecive of their physical location in the network.