  We consider the superexchange in `frustrated' Jahn-Teller systems, such as
the transition metal oxides NaNiO_2, LiNiO_2, and ZnMn_2O_4, in which
transition metal ions with doubly degenerate orbitals form a triangular or
pyrochlore lattice and are connected by the 90-degree metal-oxygen-metal bonds.
We show that this interaction is much different from a more familiar exchange
in systems with the 180-degree bonds, e.g. perovskites. In contrast to the
strong interplay between the orbital and spin degrees of freedom in
perovskites, in the 90-degree exchange systems spins and orbitals are
decoupled: the spin exchange is much weaker than the orbital one and it is
ferromagnetic for all orbital states. Due to frustration, the mean-field
orbital ground state is strongly degenerate. Quantum orbital fluctuations
select particular ferro-orbital states, such as the one observed in NaNiO_2. We
also discuss why LiNiO_2 may still behave as an orbital liquid.
