  We study the sensitivity limits of a broadband gravitational-waves detector
based on dual resonators such as nested spheres. We determine both the thermal
and back-action noises when the resonators displacements are read-out with an
optomechanical sensor. We analyze the contributions of all mechanical modes,
using a new method to deal with the force-displacement transfer functions in
the intermediate frequency domain between the two gravitational-waves sensitive
modes associated with each resonator. This method gives an accurate estimate of
the mechanical response, together with an evaluation of the estimate error. We
show that very high sensitivities can be reached on a wide frequency band for
realistic parameters in the case of a dual-sphere detector.

General Relativity and Quantum Cosmology