The electronic and molecular structures of both the ground state and some excited states of zinc carbyne and zinc stannyne have been investigated using ab initio Hartree-Fock second order Moller-Plesset (MP2) and complete active space self-consistent-field (CASSCF) calculations. The ground state of HZnCH is the triplet (3) Sigma(-) in agreement with experiment and previous theoretical work, while the first excited state, the (1) Delta state, shows a classical distortion of the Renner-Teller type. The bond mechanism in these compounds has been carefully analyzed, and particularly the possibility of the presence of a Zn-C double bond is discussed. In contrast with zinc carbyne, the ground state of zinc stannyne is a singlet (1)A’ while the first excited state is a triplet (3)A ". These states can be viewed as arising from nonclassical distortions featured by the corresponding (3) Sigma(-) and (1) Delta states due to strong electronic coupling. This loss of linearity has been related to the split between s-p tin levels and with the models proposed for nonclassical distortions at multiple bonds.