The role of core excitations in exotic nuclei is discussed in the framework of a microscopic cluster model. This cluster approach is complemented by the R-matrix theory to take account of the long-range part of the wave functions. We briefly describe the model, and present two recent examples: the neutron-rich nucleus 16 B, described by a 15 B+n structure, and the proton-rich nucleus 17 Na, described by a 16 Ne+p structure. In both cases core excitations are shown to play an important role.