Abstract The papers focusing on dynamic identification of structural damages usually rely on the comparison of two or more responses of the structure; the measure of damage is related to the differences of the vibration signals. Almost all literature methods assume damping proportionality to mass and stiffness; however, this is acceptable for new, undamaged structures, but not for existing, potentially damaged structures, especially when localised damages occur. It is well-known that in non-proportionally damped systems the modes are no longer the same of the undamped system: thus, some authors proposed to use modal complexity as a damage indicator. This contribution presents a perturbation approach that can easily reveal such a modal complexity.