Co thin films grown by thermal evaporation have been oxidized in-situ, in ambient conditions, as well as using a plasma device. In all cases, the hysteresis loops reveal exchange-bias coupling between the Co and the CoO layers. We show that the CoO/Co systems fabricated under ambient conditions and in a pure oxygen atmosphere couple magnetically in a similar way. Contrary, the CoO layer produced by plasma treatment shows a lower bias field, coercive field and blocking temperature. The systems also exhibit asymmetric hysteresis loops with different magnetization reversal for the lower descending and upper ascending magnetization branches. In one direction of the external magnetic field sweep the CoO/Co system switches mainly by domain wall motion, while for the opposite field, the influence of the coherent magnetization rotation on the reversal process is stronger. The magnitude of the asymmetry is dependent on the measurement temperature.