The wide bandgap polar semiconductors GaN and ZnO and their related alloys exhibit fascinating properties in terms of bandgap engineering, carrier confinement, internal polarisation fields, and surface terminations. With a small lattice mismatch of ∼1.8 % between GaN and ZnO and the possibility to grow MgZnO lattice-matched to GaN, the system AlGaN/MgZnO offers the opportunity to design novel optoelectronic devices circumventing the problem of p-type doping of ZnO. In such AlGaN/MgZnO heterostructures with either hetero- or isovalent interfaces, tuning of band offsets is possible in various ways by polarisation fields, surface termination, strain, and composition. These aspects need to be fully understood to be able to make full use of this class of heterostructures. We report on the growth of ZnO films by chemical vapor deposition on p-type GaN and AlGaN grown by metal-organic vapor deposition on sapphire templates and on the fabrication of corresponding light-emitting diode (LED) structures. Electrical and optical properties of the n ZnO/p-GaN and n-ZnO/p-AlGaN LEDs will be compared and the observed differences will be discussed in terms of the band alignment at the heterointerface.