Thin films of ZnO and MgxZn1-xO were epitaxially grown on Zn-polar ZnO substrates by plasma assisted molecular beam epitaxy. The miscut of c-plane ZnO substrates toward the [1-100] axis direction leads to a flat substrate surface with straight step edges. The growth mode of epitaxial ZnO films significantly depended on the growth temperature, and a substrate temperature over 800°C was needed for flat film surfaces with monolayer-height steps. Photoluminescence (PL) peak originating from the n = 2 state of A-free excitons was observed at 12 K for the ZnO films grown under stoichiometric and O-rich growth conditions. MgxZn1-xO films were also fabricated under Zn-rich conditions. The film surface exhibited a step-and-terrace structure. The effective PL lifetime of Mg 0.08Zn0.92O film was as long as 1.9 ns, which is the highest value ever reported, presumably due to a high purity level of the film.