Metamorphosis is defined as a complete change of shape, structure or substance of something. This common sense dictionary definition corresponds to the three main forms of information that must be represented in object models: geometry, topology and properties. This dissertation attempts to describe and analyze the metamorphosis problem in Rn, through the use of objects general enough to encompass, in essence, all classical forms of representation in R2 and R3. Existing techniques are analyzed as subcases of the generalization, integrating the treatment given to the previously dissociated 2D and 3D metamorphosis problems, and allowing the sharing of some of the techniques. A new approach for 3D metamorphosis, based on a 2D technique, and an implementation are described. (An English version is available from the author: lucia@visgraf.impa.br)