Context. HCG 31 is one of the most intriguing compact groups in Hickson's catalogue. It contains a central pair of interacting dwarf galaxies and other small members that are highly peculiar. Aims. The main goal of this study is to investigate the evolutionary stage of the group and measure the internal kinematics of the individual galaxies and of the possible tidal dwarf galaxies. Methods. We obtained new Fabry-Perot data cubes, including Hα images, velocity fields, velocity dispersion maps, lambda maps, position-velocity plots and rotation curves. We have taken advantage of the high spatial (sampling of ∼0.4 arcsec) and spectral (velocity sampling of ∼3 km s −1 ) resolutions of our Fabry-Perot data. Results. Kinematic peculiarities and overlapping double velocity components are measurable throughout the velocity field of A+C, with no signature of either distinct rotating disks or a single rotating galaxy. The velocity dispersion map shows widespread lowvelocity values throughout the group (consistent with the turbulent velocity of the gas), except in a narrow interface between A and C, where the merging may be occurring. The velocity curves of four candidate tidal dwarf galaxies (regions E, F, A1, and A2) show flat velocity patterns in two cases (A1 and F) and gradients with amplitudes of A ∼ 30−40 km s −1 in two others (E and A2). Our measurements show good agreement with previous optical literature data, but our data set has a much improved velocity sampling and deeper coverage. Moreover, within the star-forming regions of the group, our data profit from the higher spatial resolution with respect to HI data. Conclusions. The dynamics of the A+C system, with two main velocity components of approximately the same intensities, indicate that it is in a pre-merger stage. The two disks, in a bound orbit and in the process of merging, have had at least one earlier passage. They rotate with almost parallel spin axes like a set of gear wheels. This prograde encounter and the high star-formation rates favor the formation of a new disk. Object F may turn into a tidal dwarf galaxy bound to the group.