One of the most exciting features of the hole centers CuO₄^5- in doped cuprates is in their unusually complicated ground state as a result of electronic quasi-degeneracy. An additional hole, doped to the basic CuO₄^6- cluster with the b_1g hole can occupy both the same hybrid Cu3d-O2p orbital state resulting in a Zhang-Rice singlet ¹A_1g and the purely oxygen e_u molecular orbital resulting in singlet or triplet ^1,3E_u  term with the close energies. We present a detailed analysis of the (pseudo)-Jahn-Teller effect driven by the near-degeneracy within the (¹A_1g, ^1,3E_u)-manifold.