We present VLA D-array H i observations of the RSCG 42 and FGC 1287 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 H i extending over as much as 200 kpc in both groups. Our new, higher resolution observations reveal that the complex H i features detected by Arecibo are in reality two extraordinary long H i tails extending for ∼160 and 250 kpc, respectively, i.e. among the longest H i structures ever observed in groups of galaxies. Although in the case of RSCG 42 the morphology and dynamics of the H i 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 FGC 1287. This galaxy displays an exceptionally long ‘dog leg’ H i 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 FGC 1287. 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 H i tail remains to be determined, our discovery highlights how little we know about environmental effects in galaxy groups.