Epitaxial β-Ga2O3 layers have been grown on β-Ga2O3 (100) substrates using metal-organic vapor phase epitaxy. Trimethylgallium and pure oxygen or water were used as precursors for gallium and oxygen, respectively. By using pure oxygen as oxidant, we obtained nano-crystals in form of wires or agglomerates although the growth parameters were varied in wide range. With water as an oxidant, smooth homoepitaxial β-Ga2O3 layers were obtained under suitable conditions. Based on thermodynamical considerations of the gas phase and published ab initio data on the catalytic action of the (100) surface of β-Ga2O3 we discuss the adsorption and incorporation processes that promote epitaxial layer growth. The structural properties of the β-Ga2O3 epitaxial layers were characterized by X-ray diffraction pattern and high resolution transmission electron microscopy. As-grown layers exhibited sharp peaks that were assigned to the monocline gallium oxide phase and odd reflections that could be assigned to stacking faults and twin boundaries, also confirmed by TEM. Shifts of the layer peak towards smaller 2θ values with respect to the Bragg reflection for the bulk peaks have been observed. After post growth thermal treatment in oxygen-containing atmosphere the reflections of the layers do shift back to the position of the bulk β-Ga2O3 peaks, which was attributed to significant reduction of lattice defects in the grown layers after thermal treatment.