The vibronic problems appearing in manifolds of the electronic terms of C-60 anions are studied. It is shown that the vibronic coupling of the T-1u molecular orbital with the h(g) vibrations induces pseudo-Jahn-Teller and Jahn-Teller couplings within the electronic terms. The resulting vibronic distortions are determined by the interplay of interelectronic and vibronic interactions. In certain cases the vibronic interaction of excited electronic terms can change the spin multiplicity of the ground state.