In this paper, we study if T is an (m, C)-isometric operator and CT * C commutes with T, then T * is an (m, C)-isometric operator. We also give local spectral properties and spectral relations of (m, C)-isometric operators, such as property (β), decomposability, the single-valued extension property and Dunford's boundedness. We also investigate perturbation of (m, C)-isometric operators by nilpotent operators and by algebraic operators and give some properties.