Theoretical calculations of the low lying excited states of the Zn atom and ZnH molecule are reported. An averaged relativistic effective core potential is used for the 1s(2) 2s(2) 2p(4) 3d(10) electrons; of Zn and the polarization and intrashell correlation effects are treated with a semiempirical core polarization potential. Spin-orbit splittings are incorporated into the correlated electronic states.