One of the most exciting features of the hole centers CuO45- in doped cuprates is in their unusually complicated ground state as a result of electronic quasi-degeneracy. An additional hole, doped to the basic CuO46- cluster with the b1g hole can occupy both the same hybrid Cu3d-O2p orbital state resulting in a Zhang-Rice singlet 1A1g and the purely oxygen eu molecular orbital resulting in singlet or triplet 1,3Eu  term with the close energies. We present a detailed analysis of the (pseudo)-Jahn-Teller effect driven by the near-degeneracy within the (1A1g, 1,3Eu)-manifold.