Adaptation techniques for multimedia presentations are mainly concerned with switching between different qualities of single media elements to reduce the data volume and by this to adapt to limited presentation resources. This kind of adaptation, however, is limited to an inherent lower bound, i.e., the lowest acceptable technical quality of the respective media type. To overcome this limitation, we propose cross-media adaptation in which the presentation alternatives can be media elements of different media type, even different fragments. Thereby, the alternatives can extremely vary in media type and data volume and this enormously widens the possibilities to efficiently adapt to the current presentation resources. However, the adapted presentation must still convey the same content as the original one, hence, the substitution of media elements and fragments must preserve the presentation semantics. Therefore, our cross-media adaptation strategy provides models for the automatic augmentation of multimedia documents by semantically equivalent presentation alternatives. Additionally, during presentation, substitution models enforce a semantically correct information flow in case of dynamic adaptation to varying presentation resources. The cross-media adaptation strategy allows for flexible reuse of multimedia content in many different environments and, at the same time, maintains a semantically correct information flow of the presentation.