A mathematical model has been developed that describes the transport of species across amorphous and single-crystal solid electrolytes during ac impedance experiments. The analysis is based on the multicomponent transport equation, and it includes not only the effects of ion-pairing reactions but also the possibility that a second, nonconducting phase is distributed through the electrolyte. Transient and steady-periodic equations for the low-frequency impedance are derived for concentrated binary and ternary electrolytes sandwiched between electrodes at which an electrochemical reaction takes place. General analytic expressions are presented which relate the characteristics of the impedance response to the diffusion coefficient(s) and transference number(s) representative of the solid ionic conductor. The results show that transient effects are usually small but that species interactions and activity coefficient corrections can significantly influence the steady-periodic impedance. Accurate information on reaction stoichiometries and the nature of the mobile species is a prerequisite for meaningful interpretation of the transport properties. With the model, consistency tests are established that help distinguish between dilute and concentrated electrolytes and also that indicate when the material should be treated as a four-species system rather than as a binary electrolyte. The utility of the approach is illustrated by comparing theoretical results with available experimental data for two solid polymer electrolytes.) unless CC License in place (see abstract). ecsdl.org/site/terms_use address. Redistribution subject to ECS terms of use (see 129.170.195.149 Downloaded on 2015-01-02 to IP ) unless CC License in place (see abstract). ecsdl.org/site/terms_use address. Redistribution subject to ECS terms of use (see 129.170.195.149 Downloaded on 2015-01-02 to IP ) unless CC License in place (see abstract). ecsdl.org/site/terms_use address. Redistribution subject to ECS terms of use (see 129.170.195.149 Downloaded on 2015-01-02 to IP ) unless CC License in place (see abstract). ecsdl.org/site/terms_use address. Redistribution subject to ECS terms of use (see 129.170.195.149 Downloaded on 2015-01-02 to IP