  I develop a microscopic three-cluster model for exotic light nuclei. I use
the hyperspherical formalism, associated with the Generator Coordinate Method.
This model is well adapted to halo nuclei, since the long-range part of the
radial wave functions is accurately reproduced. The core wave functions are
described in the shell model, including excited states. This technique provides
large bases, expressed in terms of projected Slater determinants. Matrix
elements involve seven-dimension integrals, and therefore require long
calculation times. I apply the model to 11Li, 14Be, 15B, and 17N described by
two neutrons surrounding a 9Li, 12Be, 13B and 15N core, respectively. The 17Ne
(as 15O+p+p) and 15Ne (as 13O+p+p) mirror nuclei are briefly discussed. I
present the spectra and some spectroscopic properties, such as r.m.s. radii or
E2 transition probabilities. I also analyze the importance of core excitations.
