Conventional data envelopment analysis (DEA) treats a system as a whole unit when measuring efficiency, ignoring the operations of the component processes. Network DEA, on the other hand, takes the component processes into consideration, with results that are more representative and can be used to identify inefficient components. This paper discusses network DEA for fuzzy observations. Two approaches, the membership grade and the α-cut, are proposed for measuring the system and process efficiencies via two-level mathematical programming. The model associated with the latter approach is transformed into a conventional one-level program so that the existing solution methods can be applied. Since the data is fuzzy, the measured efficiencies are also fuzzy. The property of the system efficiency slack being the sum of the process efficiency slacks, which holds in the deterministic case, was found to hold for the fuzzy case as well. A simple network system with three processes is used to illustrate the proposed idea.