The velocity field of the central parts of the elliptical galaxy NGC 7626 has been mapped by obtaining high resolution curves and velocity dispersion profiles for four slit position angles along the major, minor and two intermediate photometric axes. Each rotation curve and dispersion profile shows a high level of structure. Along the major axis, the rotation curve reverses sign twice at each side of the center. Along the minor axis, we find a velocity reversal at the core plus two narrow (approximately 1 arcsec) regions of velocity reversal further out, symmetrically placed with respect to the center. Similar narrow features seen along other position angles suggest that we have detected shells kinematically. We tentatively identify three kinematic regions, the core, the intermediate region and the outer part. The rotation axis of the core lies at 45 deg from the photometric major axis. The spin of the intermediate region is opposite to that of the core, and that of the outer part is roughly orthogonal. The core is not dynamically relaxed. A merger/accretion is thus the most plausible origin for the peculiar kinematics. The many dynamical components make NGC 7626 an outstanding example of a core in the making. We analyze this system to infer clues on late merger dynamics. The merger appears to increase the tangential velocity dispersion and contribute to flatten the velocity dispersion profile. We speculate that, once the system relaxes, orthogonal core and main body rotation may be stabilized by long- and short-axis tube orbits. We suggest that mergers may establish the net circulation in tube orbits which is responsible for the kinematic twists in the projected velocity fields of triaxial galaxies. The dynamical age of the core is at most 108 years. A starburst of this age would be expected to leave a signature in the spectrum of the galaxy, hence we can rule out a starburst at a time of onset of the peculiar kinematic features.