  We investigate the dynamical evolution of the potentially habitable
super-earth GJ 667Cc in the multiple system of at least two exoplanets orbiting
a nearby M dwarf, paying special attention to its spin-orbital state. The
published radial velocities for this star are re-analyzed and evidence is found
for additional periodic signals, which could be taken for two additional
planets on eccentric orbits. Such systems are not dynamically viable and break
up quickly in numerical integrations. Limiting the scope to the two originally
detected planets, we assess the dynamical stability of the system and find no
evidence for bounded chaos in the orbital motion. The orbital eccentricity of
the planets b and c is found to change cyclicly in the range 0.06 - 0.28 and
0.05 - 0.25, respectively, with a period of approximately 0.46 yr. Taking the
eccentricity variation into account, numerical integrations are performed of
the differential equations modeling the spin-orbit interaction of the planet GJ
667Cc with its host star assuming a terrestrial composition of its mantle.
Depending on the interior temperature of the planet, it is likely to be
entrapped in the 3:2 (probability 0.51) or even higher spin-orbit resonance. It
is less likely to reach the 1:1 resonance (probability 0.24). The estimated
characteristic spin-down times are quite short for the two planets, i.e.,
within 1 Myr for planet c and even shorter for planet b. Both planet arrived at
their current and, most likely, ultimate spin-orbit states a long time ago. The
rate of tidal dissipation of energy is formidably high in the planets of GJ
667, estimated at $10^{23.7}$ and $10^{26.7}$ J yr$^{-1}$ for c and b,
respectively. This raises a question of how such relatively massive, close
super-Earths could survive overheating and destruction.
