The structuring of the specification and development of distributed systems according to viewpoints, as advocated by the Reference Model for Open Distributed Processing, raises the question of when such viewpoint specifications may be considered consistent with one another. In this paper, we analyse the notion of consistency in the context of formal process specification. It turns out that different notions of correctness give rise to different consistency relations. Each notion of consistency is formally characterised and placed in a spectrum of consistency relations. An example illustrates the use of these relations for consistency checking.