This work aims to extend the algebraic single-pushout approach to graph transformation to model object-oriented systems structures and computations. Graphs whose sets of nodes and edges are partially ordered are used to model the class hierarchy of an object-oriented system, making the inheritance and overriding relations explicit. Graphs typed over such structures are then used to model systems of objects, whose behaviour is given by an object-oriented graph grammar. It will be shown how the derivations which arise from those grammars are compatible with the way object-oriented programs are defined and executed.