Crystals of Na+-beta"-Al2O3 and Na+/Ho3+-beta"-Al2O3, with varying degrees of exchange, have been investigated by impedance spectroscopy using sputtered chromium films as electrodes. For this work a sample holder was developed to enable studies of the in-plane conductivity of even very thin beta"-alumina crystals. The ionic conductivities of the investigated Na+-beta"-Al2O3 crystals were found to be one order of magnitude lower than those reported in the literature, a discrepancy caused by a lower charge carrier concentration. On the other hand, the activation energy and the diffusion coefficients of the sodium ions, as deduced from the Nernst-Einstein equation, agree well with previous studies. In the case of the Na+/Ho3+-beta"-Al2O3 crystals, a strong decrease of the ionic conductivity has been observed with increasing degree of exchange. To determine the bulk conductivities an equivalent circuit had to be applied which differed from the one used in case of Na+-beta"-Al2O3. With an additional RC-element in parallel these spectra could be fitted with satisfying results. This RC-element may be regarded as a second relaxation process of the Na+ ions.