One of the most exciting features of the hole centers CuO 5− 4 in doped cuprates is an unusually complicated ground state which is the result of the electronic quasi-degeneracy. An additional hole, doped to the basic CuO 6− 4The Jahn-Teller hole centers like CuO 5− 4 with singlet-triplet quasi-degeneracy within ground state have been observed by ESR spectroscopy in LaSrAl 1−x Cu x O 4 which is isostructural to La 2−x Sr x CuO 4 [5]. Moreover, Yu. Yablokov et al. [6] conjectured that doped hole in the copper-oxygen clusters occupies a purely oxygen a 2g (π), or b 2u (π) like orbitals. An important indication to the O2p(π) nature of doped holes and, hence, to the occurrence of near-degeneracy for configurations like b 2 1g and b 1g e u (π) was obtained by Yoshinari [7] and Martindale et al. [8] after the analysis of the 17 O Knight shift data and temperature-dependent anisotropy of the planar oxygen nuclear spinlattice relaxation rate in Y Ba 2 Cu 3 O 6+x , respectively. Analogous conclusion could be drawn out of the comparative analysis of the temperature behavior for the nuclear spin-lattice relaxation rate in La 2−x Sr x CuO 4 [9]. All this implies a complicated nature of the ground state manifold for the CuO 4 center with a significant mixing of the Zhang-Rice singlet and some other molecular term, which symmetry should be distinct from 1 A 1g . This conclusion conflicts with the widespread opinion regarding the well isolation of the Zhang-Rice singlet.An important argument in favor of vibronic nature for ground state of CuO 4 clusters with the participation of e uorbitals in the 123 system was obtained after analysis of experimental data on EFG (electric field gradient) tensor for different nuclei in 123 system [10]: non-contradictory description of the data implies a considerable (10%!) difference in electron density for O(2) and O(3) oxygens. It is unlikely that this result could be obtained without PJT effect.These and many other results of resonance (ESR, NQR/NMR) experiments being precise local probes cast doubt on the validity of popular conceptions which are widely used as a starting point for the analysis of resonance and in broader sense for many other physical effects in cuprates.A considerable number of the experimental indications of Jahn-Teller (vibronic) effects is associated with observation of lattice instabilities, ferroelectric [11], pyro-and piezoelectric [12] anomalies, local static and dynamic distortions [13], various phonon anomalies and manifestation of substantial electron-phonon effects such as the line shift and Fano effect for the phonon modes associated with local PJT-active modes [14][15][16]. These observations and many other lattice effects are signatures of unconventional strong electron-lattice interaction at work in the cuprates [13] with highly nonlinear and nonadiabatic intrinsic dynamics. Up to now these phenomena are often considered as convincing evidence in favour of the "structural" scenario for the high-T c superconductivity usually associated with polarons (pseu...