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Both non-determinism and multi-level networks compactly characterize the flexibility allowed in implementing a circuit. A theory for representing and manipulating non-deterministic (ND) multi-level networks is developed. The theory supports all the network manipulations commonly applied to deterministic binary networks, such as node minimization, elimination, and decomposition. It is shown that an ND network's behavior can be interpreted in three ways, all of which coincide when the network is deterministic. Operations performed on an ND network are analyzed under each interpretation for changes in a network's behavior. Modifications of a few operations are given which must be used to guarantee that a network's behavior does not violate its external specification. These modifications depend on which behavior is being used and the location of related non-determinism. This theory has been implemented in a system, MVSIS. We provide comparisons among the uses of the various behaviors.