[en] Triple graph grammars (TGGs) are a formal and intuitive concept for the specification of model transformations. Their main advantage is an automatic derivation of operational rules for bidirectional model transformations, which simplifies specification and enhances usability as well as consistency. In this paper we continue previous work on the formal definition of model transformations based on triple graph rules with negative application conditions (NACs). The new notion of partial source consistency enables us to construct consistent model transformations on-the-fly instead of analyzing consistency of completed model transformations. We show the crucial properties termination, correctness and completeness (including NAC-consistency) for the model transformations resulting from our construction. Moreover we define parallel independence for model transformation steps which allows us to perform partial-order reduction in order to improve efficiency. The results are applicable to several relevant model transformations and in particular to our example transformation from class diagrams to database models.