Medical images that are to be registered for clinical application often contain both structures that deform and ones that remain rigid. Nonrigid registration algorithms that do not model properties of different tissue types may result in deformations of rigid structures. In this article a local rigidity penalty term is proposed which is included in the registration function in order to penalize the deformation of rigid objects. This term can be used for any representation of the deformation field capable of modelling locally rigid transformations. By using a B-spline representation of the deformation field, a fast algorithm can be devised. The proposed method is compared with an unconstrained nonrigid registration algorithm. It is evaluated on clinical three-dimensional CT follow-up data of the thorax and on two-dimensional DSA image sequences. The results show that nonrigid registration using the proposed rigidity penalty term is capable of nonrigidly aligning images, while keeping user-defined structures locally rigid.