Distributed diagnosis is important for complex systems as a way to reduce computational costs or for large systems that require minimizing data transfer. This paper presents a distributed diagnosis method for continuous systems that only requires the knowledge of local models and limited knowledge of their neighboring subsystems. The notion of Fault-Driven Minimal Structurally Overdetermined (FMSO) set is used as the corner stone of the design of residual generators. We show that all the FMSO sets of the global system can be obtained in a distributed manner from so-called shared FMSO sets and shared CMSO sets that are computed along a structural approach for every local site.