  The Darwin-Kaula theory of bodily tides is intended for celestial bodies
rotating without libration. We demonstrate that this theory, in its customary
form, is inapplicable to a librating body. Specifically, in the presence of
libration in longitude, the actual spectrum of Fourier tidal modes differs from
the conventional spectrum rendered by the Darwin-Kaula theory for a
non-librating celestial object. This necessitates derivation of formulae for
the tidal torque and the tidal heating rate, that are applicable under
libration.
  We derive the tidal spectrum for longitudinal forced libration with one and
two main frequencies, generalisation to more main frequencies being
straightforward. (By main frequencies we understand those emerging due to the
triaxiality of the librating body.) Separately, we consider a case of free
libration at one frequency (once again, generalisation to more frequencies
being straightforward).
  We also calculate the tidal torque. This torque provides correction to the
triaxiality-caused physical libration. Our theory is not self-consistent: we
assume that the tidal torque is much smaller than the
permanent-triaxiality-caused torque; so the additional libration due to tides
is much weaker than the main libration due to the permanent triaxiality.
  Finally, we calculate the tidal dissipation rate in a body experiencing
forced libration at the main mode, or free libration at one frequency, or
superimposed forced and free librations.
