Growth control of nonpolar and polar ZnO/MgxZn1-xO quantum wells (QWs) is demonstrated by in situ RHEED during the pulsed laser deposition process. Nonpolar QWs were grown homoepitaxially on m-plane and on a-plane ZnO single crystals. For m-plane (10 (1) over bar0) ZnO QWs we report a change of growth mode from a two dimensional layer by layer growth evidenced by RHEED oscillations to the formation of surface nanostripes as observed by atomic force microscopy. The aspect ratio of the self organized nanostripes depends on the oxygen partial pressure. a-lane (11 (2) over bar0) ZnO QW-structures show a smooth surface with a rms-roughness of 0.3 nm. Homoepitaxial nonpolar QWs do not show the quantum-confined Stark effect while polar quantum wells on a-plane sapphire does with an internal electric field of approximately 0.53 MV/cm. Furthermore, by implementing a low temperature MgxZn1-xO buffer layer, the interface quality of heteroepitaxially grown polar ZnO/MgxZn1-xO QWs on a-plane sapphire substrates is considerably improved. RHEED oscillations were observed during the whole growth of such QWs. (C) 2012 Elsevier B.V. All rights reserved.