Time-dependent density-functional theory (TDDFT) is used to study the excitation energies of the global minima of small ZniOi clusters, i = 1-15. The relativistic compact effective core potentials and shared-exponent basis set of Stevens, Krauss, Basch, and Jasien (SKBJ), systematically enlarged with extra functions, were used throughout this work. In general, the calculated excitations occur from the nonbonding p orbitals of oxygen. These orbitals are perpendicular to the molecular plane in the case of the rings and normal to the spheroid surface for 3D clusters. The calculated excitation energies are larger for ringlike clusters as compared to 3D clusters, with the excitation energies of the latter structures lying close to the visible spectrum. The difference between Kohn-Sham eigenvalues of the orbitals involved in the electronic excitations studied have also been compared to the TDDFT results of the corresponding excitations for two approximate density functionals, that is, MPW1PW91 and B3LYP, the latter being more accurate. Moreover, they approach the TDDFT value as the cluster size increases. Therefore, this might be a practical method for estimating excitation energies of large ZniOi clusters.