We investigate the spin-orbital evolution of the potentially habitable super-Earth GJ 667Cc in the multiple system of at least two exoplanets orbiting a nearby M dwarf. 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 making the system dynamically inviable. 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 cyclically 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 spin-orbit interactions 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. The rate of tidal dissipation of energy in the planets of GJ 667 is estimated at 1023.7 and 1026.7 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.
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