The incremental development of software systems involves the detection and handling of inconsistencies. These inconsistencies arise in system requirements, design specifications and, quite often, in the final implemented software product. In this paper we explore different kinds of inconsistency that arise during different stages of software development, and examine the scope and role of computer-based tool support for managing inconsistency in this setting. In addition to detecting and removing inconsistencies, managing inconsistency also includes a wide range of activities that facilitate continued development in the presence of inconsistency. These include procedures for controlled amelioration and avoidance of incosistencies. The paper uses the ViewPoints framework for multi-perspective software development as a vehicle for the discussion, and as a test bed for tool support. The framework facilitates the development and composition of multiple partial specifications (ViewPoints), and is itself supported by automated tools that check and handle inconsistencies (The Viewer). The paper makes a contribution towards a better understanding of the way in which complex software systems are developed, and consequently, the kind of automated tool support that needs to be provided in this setting.