Renormalizability and searching for Z' gauge bosons

New observables for searching for Z' virtual states in processes e^+e^-\to\bar{f}f are proposed. They are based on the relations following due to renormalizability of an underlying theory between the parameters of the low-energy effective Lagrangian. Two types of the Z' interactions are considered. The observables allow to pick up uniquely the signals of both Z' bosons. The search for the Z' at future linear colliders and the treating of the LEP data are discussed.