Results are presented on the comparative oxidation behaviour of Co1-deltaO into Co3O4 at 800 degrees C for single crystals and aligned eutectic CoO-ZrO2(CaO) samples exhibiting different deviations from stoichiometry, delta, before oxidation. We show, in particular, that depending on the physicochemical and thermal history of the samples, parabolic laws of oxidation are or are not observed. It is shown that this behaviour is directly related to the value of delta and we propose a simple model which accounts for the observed data. In single crystalline and aligned eutectics samples, if delta is higher than delta* = 5 x 10(-3) (delta* is the 800 degrees C equilibrium deviation from stoichiometry of Co1-deltaO in equilibrium with Co3O4), oxidation is controlled by ionic transport of cobalt ions in Co3O4 and a parabolic law is observed. When delta is smaller than delta*, oxidation of single crystalline CoO results in the simultaneous formation of Co3O4 on the surface of CoO and partial dissolution of the Co3O4 layer by CoO which has to change into Co-1-delta. O. This complex behaviour results in a non-parabolic oxidation law, the oxidation process being slower than that relative to the parabolic prediction. CoO-ZrO2(CaO) aligned eutectics do not follow the same kinetic behaviour because the calcia-stabilized zirconia (CSZ) acts as an oxygen short circuit which allows CoO to equilibrate very rapidly into Co-1-delta. O everywhere in the sample, allowing parabolic formation of Co3O4.