Like other software artefacts, metamodels evolve over time. We propose a transformational approach to assist metamodel evolution by stepwise adaptation. In the first part of the paper, we adopt ideas from grammar engineering to define several semantics- and instancepreservation properties in terms of metamodel relations. This part is not restricted to any metamodel formalism. In the second part, we present a library of QVT Relations for the stepwise adaptation of MOF compliant metamodels. Transformations from this library separate preservation properties. We distinguish three kinds of adaptation according to these properties; namely refactoring, construction, and destruction. Coadaptation of models is discussed with respect to instance-preservation. In most cases, co-adaptation is achieved automatically. Finally, we point out applications in the areas of metamodel design, implementation, refinement, maintenance, and recovery.