The character of the low-lying excited states of diatomic CuCl is studied primarily by means of the complete active space self-consistent field (CASSCF), method and a second order perturbation approach with the CASSCF wave function as reference state [complete active space perturbation theory to second order (CASPT2)]. Far comparison, the lower levels of the spectra of the Cu+ ion are also analyzed. A first order treatment of the scalar relativistic effects, the mass-velocity and Darwin terms, is included in the calculations. The importance of spin-orbit interactions is investigated by comparing our nonrelativistic valence shell CI (VCI) and relativistic results obtained with our four-component program suite MOLFDIR. The six lowest excited states of the CuCl molecule, which are related to the Cu+(3d(9)4s(1))Cl-(3s(2)3p(6)) ionic configuration, are assigned. The assignments agree with earlier theoretical work. Where they can be compared, the calculated spectroscopic constants are in good agreement with the experimental data.