We present VLA D-array HI observations of the RSCG42 and FGC1287 galaxy groups, in the outskirts of the Abell 1367 cluster. These groups are projected ~ 1.8 and 2.7 Mpc west from the cluster centre. The Arecibo Galaxy Environment survey provided evidence for HI extending over as much as 200kpc in both groups. Our new, higher resolution observations reveal that the complex HI features detected by Arecibo are in reality two extraordinary long HI tails extending for ~160 and 250 kpc, respectively, i.e., among the longest HI structures ever observed in groups of galaxies. Although in the case of RSCG42 the morphology and dynamics of the HI tail, as well as the optical properties of the group members, support a low-velocity tidal interaction scenario, less clear is the origin of the unique features associated with FGC1287. This galaxy displays an exceptionally long dog leg HI tail and the large distance from the X-ray emitting region of Abell 1367 makes a ram-pressure stripping scenario highly unlikely. At the same time a low-velocity tidal interaction seems unable to explain the extraordinary length of the tail and the lack of any sign of disturbance in the optical properties of FGC1287. An intriguing possibility could be that this galaxy might have recently experienced a high-speed interaction with another member of the Coma-Abell 1367 Great Wall. We searched for the interloper responsible for this feature and, although we find a possible candidate, we show that without additional observations it is impossible to settle this issue. While the mechanism responsible for this extraordinary HI tail remains to be determined, our discovery highlights how little we know about environmental effects in galaxy groups.