The results of the impedance spectroscopy measurements on eutectic samples based on zirconium oxide are presented here. Samples of CaZrO3-ZrO2(cubic) and MgO-ZrO2(cubic) have been grown by a directional solidification procedure such that the different phases appear nearly oriented along the growth direction (lamellae in the system of CaZrO3-ZrO2(cubic) and fibers of MgO in a ZrO2 matrix in the other system). The DC electrical conductivity has been measured by impedance spectroscopy along and across the growth axis. For CaZrO3-ZrO2 the coductivity is clearly anisotropic. The following values for sigma T have been obtained : the conductivity at 600 degrees C equals 2.0 x 10(-6) Omega(-1) cm(-1) perpendicular to the fiber axis and 1.4 x 10(-5) Omega(-1) cm(-1) parallel to it and with an activation energy of 1.3 eV for sigma T. For MgO-ZrO2(cubic) the isotropic value of the conductivity at 600 degrees C is 10(-4) Omega(-1) cm(-1) with activation energy for sigma T of 1.5 eV. The anisotropic conductivity in the CaZrO3-ZrO2(cubic) system has been explained by a model of an ordered stacking of oxygen conducting (cubic ZrO2) and non-conducting (CaZrO3 or MgO) phases.