We are studying the optical spectra of impurity centers in the case when the optical transition takes place between nondegenerate and two-fold degenerate electronic E-states characterized by a strong vibronic coupling. In the latter state the adiabatic surface has a shape of a deformed Mexican hat with three flat minima on the trough of the "hat." We have found that in this case the usual T-7-dependence of the homogeneous width of the zero-phonon line at low temperatures is replaced by a dependence close to the T-3-one. Besides, the usual T-4-dependent redshift of the line is replaced by the T-2-dependent shift. Depending on the flatness of the adiabatic surface, the latter shift may be to the red or to the blue. The theory is applied to the zero-phonon line 637 nm of the nitrogen-containing N-V center in a diamond. In this system the temperature dependence of the ZPL results from the common action of the Jahn-Teller effect and the pseudo-Jahn-Teller effect in the excited E-state: the pseudo-Jahn-Teller effect "helps" to get the system close to the dynamical instability due to the enlargement of the Jahn-Teller distortion. (C) 2003 American Institute of Physics.