  An analysis based on the direct torque equations including tidal dissipation
and a viscous core-mantle coupling is used to determine the damping time scales
of O(10^5) years for free precession of the spin about the Cassini state and
free libration in longitude for Mercury. The core-mantle coupling dominates the
damping over the tides by one to two orders of magnitude for the plausible
parameters chosen. The short damping times compared with the age of the solar
system means we must find recent or on-going excitation mechanisms if such free
motions are found by the current radar experiments or the future measurement by
the MESSENGER and BepiColombo spacecraft that will orbit Mercury. We also show
that the average precession rate is increased by about 30% over that obtained
from the traditional precession constant because of a spin-orbit resonance
induced contribution by the C_{22} term in the expansion of the gravitational
field. The C_{22} contribution also causes the path of the spin during the
precession to be slightly elliptical with a variation in the precession rate
that is a maximum when the obliquity is a minimum. An observable free
precession will compromise the determination of obliquity of the Cassini state
and hence of C/MR^2 for Mercury, but a detected free libration will not
compromise the determination of the forced libration amplitude and thus the
verification of a liquid core
