Abstract. The complexity of large system models in software engineering nowadays is mastered by using different views. View-based modeling aims at creating small, partial models, each one of them describing some aspect of the system. Existing formal techniques supporting view-based visual modeling are based on typed attributed graphs, where views are related by typed attributed graph morphisms. Such morphisms up to now require a fixed type graph, as well as a fixed data signature and domain. This is in general not adequate for view-oriented modeling where only parts of the complete type graph and signature are known and necessary when modeling a partial view of the system. The aim of this paper is to extend the framework of typed attributed graph morphisms to generalized typed attributed graph morphisms, short GAG-morphisms, which involve changes of the type graph, data signature, and domain. This allows the modeler to formulate type hierarchies and views of visual languages defined by...