The stability of the laminar flow in the narrow gap between infinitely long concentric cylinders, the inner of which rotates, is examined for the case of compliant bounding walls, modelled as thin cylindrical shells supported by rigid frames through arrays of springs and dampers. Sufficiently soft walls have a destabilizing influence on the axisymmetric Taylor vortices produced by the centrifugal force, although the effect is limited to modes with large axial wavelengths. Due to the walls flexibility, hydroelastic modes are generated. Complex modal exchanges are observed, as function of the wall properties and the Reynolds number. For axisymmetric modes an asymptotic analysis is conducted in the limit of small axial wavenumber, to show the correspondence between such exchanges and singularities in the analytical solutions. While the axisymmetric modes dominate the spectrum when the walls are rigid or very mildly compliant, a critical non-zero azimuthal wavenumber exists for which the hydroelastic modes become more unstable. Shorter azimuthal waves are favoured by increasing spring stiffness.