Context. Data derived from the reconstruction of the nucleus shape of comet 67P/Churyumov-Gerasimenko (67P) from images of the OSIRIS camera onboard ROSETTA show evidence that the nucleus rotates in complex mode. First, the orientation of the spin axis is not fixed in an inertial reference frame, which suggests a precessing motion around the angular momentum vector with a periodicity of approximately 257 h +/- 12 h. Second, periodograms of the right ascension and declination (RA/Dec) coordinates of the body-frame Z axis show a very significant (higher than 99.99%) periodicity at 276 h +/- 12 h, different from the rotational period of 12.40 h as previously determined from light-curve analysis. Aims. The main goal is to interpret the data and associated periodicities of the spin axis orientation in space. Methods. We analyzed the spin axis orientation in space and associated periodicities and compared them with solutions of Euler equations under the assumption that the body rotates in torque-free conditions. Statistical tests comparing the observationally derived spin axis orientation with the outcome from simulations were applied to determine the most likely inertia moments, excitation level, and periods. Results. Under the assumption that the body is solid-rigid and rotates in torque-free conditions, the most likely interpretation is that 67P is spinning around the principal axis with the highest inertia moment with a period of about 13 h. At the same time, the comet precesses around the angular momentum vector with a period of about 6.35 h. While the rotating period of such a body would be about 12.4 h, RA/Dec coordinates of the spin axis would have a periodicity of about 270 h as a result of the combination of the two aforementioned motions. Conclusions. The most direct and simple interpretation of the complex rotation of 67P requires a ratio of inertia moments significantly higher than that of a homogeneous body.