We performed a kinematical analysis of the [CII] line emission of the BR 1202-0725 system at z ∼ 4.7 using ALMA science verification observations. The most prominent sources of this system are a quasar (QSO) and a submillimeter galaxy (SMG), separated by a projected distance of about ∼24 kpc and characterized by very high star formation rates, higher than ∼1000 M yr −1 . However, the ALMA observations reveal that these galaxies apparently have undisturbed rotating disks, which is at variance with the commonly accepted scenario in which strong star formation activity is induced by a major merger. We also detected faint components which, after spectral deblending, were spatially resolved from the main QSO and SMG emissions. The relative velocities and positions of these components are compatible with orbital motions within the gravitational potentials generated by the QSO host galaxy and the SMG, suggesting that they are smaller galaxies in interaction or gas clouds in accretion flows of tidal streams. Moreover, we did not find any clear spectral evidence for outflows caused by active galactic nuclei or stellar feedback. This suggests that the high star formation rates might be induced by interactions or minor mergers with these companions, which do not affect the large-scale kinematics of the disks, however. Alternatively, the strong star formation may be fueled by the accretion of pristine gas from the host halo. Our kinematical analysis also indicates that the QSO and the SMG have similar dynamical masses, mostly in the form of molecular gas, and that the QSO host galaxy and the SMG are seen close to face-on with slightly different disk inclinations: the QSO host galaxy is seen almost face-on (i ∼ 15 • ), while the SMG is seen at higher inclinations (i ∼ 25 • ). Finally, the ratio between the black hole mass of the QSO, obtained from new X-shooter spectroscopy, and the dynamical mass of the host galaxy is similar to value found in very massive local galaxies, suggesting that the evolution of black hole galaxy relations is probably better studied with dynamical than with stellar host galaxy masses.