  New dielectric transitions are observed at common temperatures 32K and 245K,
in isostructural $La_{2}CuO_{4+x}$ and $La_{5/3}Sr_{1/3}NiO_{4},$ that are
signatures of local lattice (octahedral) instabilities. The present dielectric
transitions reveal new aspects of the phase diagram of the perovskite cuprates
and nickelates. They suggest that competition and coexistence of
superconductivity with dielectricity occurs that is analogous to that between
superconductivity and anti-ferromagnetism. These results also indicate that
inhomogeneous electronic states, such as charge stripes and oxygen ordering,
are strongly connected to underlying lattice instabilities.
