A rigorous mathematical model is developed for the complex impedance of a solid-state electrochemical cell, which is commonly used for the measurement of oxygen transport, oxygen exchange kinetics and thermodynamic properties of nonstoichiometric mixed conducting oxides. The model leads to a simple equivalent circuit for the cell with unambiguous definition of the physical significance of its components. A method is proposed for the analysis of experimental data. The methodology thus developed is validated by comparing the experimental data measured for a well-studied perovskite (SrCo0.5Fe0.503-delta) with the results obtained from the completely equivalent potential-step technique. In addition, various electrochemical properties of the other cell components, such as Pt electrodes and YSZ electrolyte, also obtainable from measurements, show good agreement with the available literature data. The cell design, which significantly minimizes the gas space in contact with the sample, has a clear advantage over similar relaxation cells in terms of reducing the dominating effect of the gas phase capacitance in numerical data analysis. A possible disadvantage, however, is the large impedance of the oxygen pump at low oxygen partial pressures, which may in a similar manner obstruct deconvolution of the sample properties from the measured data.