The group‐III nitride and the group‐II oxide semiconductors have direct band gaps, which cover the ultraviolet to infrared energy range. In this work we calculate the band gaps and built‐in electric field of the polar wurtzite GaN/AlN and ZnO/MgO Short Period Superlattices (SPSLs). In many respects GaN and AlN are similar to ZnO and MgO, respectively, especially regarding the band gaps and the lattice parameters. To realize the wider band gap based materials the superlattices (SLs) with GaN and ZnO as quantum wells and AlN and MgO as quantum barriers, that is, GaN/AlN and ZnO/MgO, are created. We found similar evolution of the GaN/AlN and ZnO/MgO band gaps with varying number of atomic layers constituting these SPSLs. Band gap bowings and strength of the internal electric field existing in these two families of SPSLs differ significantly.