The a.c. conductivity of the solid electrolyte beta-alumina with blocking Au electrodes has been examined by complex plane analysis using the complex impedance (Z*), admittance (A*), modulus (M*) and permittivity (epsilon*) formalisms. The electrode response which gives rise to the characteristic "spikes" in the Z* plots is attributed to a highly resistive layer on the surface of beta-alumina. This is found on single crystal and polycrystalline materials, and is sensitive both to the effects of polishing and the uptake of water vapour. Water vapour does not affect the bulk properties. For the first time, both the conductivity and the modulus spectra of single crystal beta"-alumina have been reported. It is confirmed that beta"-alumina has a much higher activation energy (~27kJ/mole) than beta-alumina (16.0kj/mole) and thus has a lower conductivity at lower temperatures (100°C). On this basis, an attempt has been made to explain the behaviour of the (commercial) polycrystalline sinters which are mixtures of beta and beta" phases. While the grain boundary activation energy remains constant at ~ 26kJ/mole, the bulk activation energy varies with beta/beta" content. The mixtures of approx 50-70% beta" content have the lowest bulk activation energy. These effects may be related in some way to the method of charge compensation, and in particular to the interstitial oxygen content (Oi2-). A "mixed-alkali" effect has been discovered in Na/Ag beta-aluminas which is remarkably similar to the effects found in glass. Both conductance minima and modulus (M") peak "narrowing" are observed. The results add some support to the weak electrolyte theory of beta-alumina, and also offer an interesting new exception to Jonscher's "universal" dielectric behaviour.