The Network Function Virtualization (NFV) virtualizes the network appliancessuch as routers and firewallswith software running on commercial off-the-shelf servers. In NFV specification, Network Services (NS) are composed of multiple Virtual Network Functions (VNF) enabling elastic and finer lifecycle management operations such as scaling. For adapting resources to the VNF-based network services evolving context, these operations require to execute, on the fly, a reconfiguration plan supervised by a central orchestrator. This is the singledomain reconfiguration, where the orchestrator has global up-to-date information, ensuring the correct execution of the lifecycle management operations. Moreover, in practice, NS can be implemented by composing VNFs in a cross-domain schema called a multi-domain federation. In this case, the reconfiguration is more challenging since there are multiple orchestrators, one by domain, that manage collaboratively shared network services. Sharing network services creates functional and non-functional dependencies among these services that must be considered for ensuring the consistency of the lifecycle operations. The consistent reconfiguration of shared network services in distributed multi-domain federations is called the NFV Dependent Reconfiguration problem. However, despite being identified as an important challenge by the NFV community, no related solution has yet been proposed. In this paper, we focus on the NFV Dependent Reconfiguration problem. We introduce a distributed approach to guarantee consistency during dependent reconfiguration. The approach is composed of a distributed multi-domain model that establishes the interactions among the federation 's entities, and a causally-consistent distributed orchestration algorithm based on such a model. We verify the algorithm viability using, as a case study, the scaling of shared VNF-based network services as defined by the current NFV standard architecture. To the best of our knowledge, the proposed distributed orchestration approach is the first that supports the consistent execution of dependent reconfiguration operations for VNF-based network services.