Electrochemical impedance spectroscopy (EIS), a well-established technique in classical electrochemistry [1], can also be very useful for the analysis of stability of electrochemical systems, including diagnosis of selected bifurcations. Impedance spectra of such dynamical systems allow also classify electrochemical oscillators into respective types. In fact, due to linearization involved in the concept of impedance, this way of the stability analysis of electric (electrochemical) circuits is a specific variant of linear stability analysis described in Sect. 1.3.In this section a short presentation of the principle of impedance measurements is described, in order to make the reader familiar with the notation used further in this chapter. The basis for this summary will be typical (Randles-type) equivalent circuit from Fig. 2.6, in which Z f will henceforth mean generally the ac impedance, measured for ac frequency f [Hz] (or angular frequency o ¼ 2pf [rad s À1 ]). The idea of such equivalent circuits, coming from the seminal work of Randles [2], was concordant with the experimental equipment used in early times of impedance measurements. It involved the ac bridge, in which one branch contained the experimental system, the impedance characteristics of which had to be balanced, in the other branch, by the impedance of the electric (equivalent) circuit, possibly closely reflecting the properties of the experimental one.Typically the electrochemical cell is first brought into steady-state, or at least quasi-steady-state (E ss , I ss ) which is further perturbed with the externally applied small amplitude, sinusoidal ac voltage (typically) or ac current. As a consequence, the electrode potential E and the current I will oscillate around their steady-state values with the same frequency o, but in general case exhibiting (frequency dependent) phase difference. In general notation one can denote the phase shifts for both the electrode potential and the current as ' 1 and ' 2 , respectively, and then:M. Orlik, Self-Organization in Electrochemical Systems I, Monographs in Electrochemistry,