An excitation function for resonance elastic scattering of alpha particles on O-18 and Ne-18 was measured using the method of inverse geometry with a very thick target. Spectroscopic information was obtained for 23 levels in the excitation energy region from 11.9 to 13.7 MeV in Ne-22. Twelve of them are new. General features of a-cluster bands in Ne-22 are analyzed in the framework of the potential model with a deep potential well. Predictions for the 11(-) level in Ne-22, as well as for the isotopic shift of the cluster levels in Mg-22, are given. Evidence is presented that new perspectives on the study of nuclear structure and nuclear spectroscopy can be obtained in complimentary measurements of alpha-cluster states in mirror Nnot equalZ nuclei.