The two-centre Jahn-Teller effect for edge- and face-shared bioctahedra with a vibronic E(g) x e(g) interaction at each centre is considered. The lowest sheet of the adiabatic potential of these systems is investigated using the one-centre-coordinate approach. It is shown that the intercentre correlation of the Jahn-Teller distortions is of great importance in these systems. This correlation is determined by the intercentre elastic interaction and, implicitly, by the coupling conditions imposed on the one-centre nuclear coordinates as a result of the presence of common atoms in the bioctahedra. Owing to the intercentre correlation, non-Jahn-Teller distortions of individual octahedra arise together with the Jahn-Teller distortions. The resulting equilibrium nuclear configurations of the bioctahedra are compared with those observed in the low-symmetry structure phase of the CuX2(NH3)2 distortion isomers and the hexagonal perovskites ACuCl3.