Designs of GaN/AlGaN quantum-cascade lasers emitting at 34 and 38 μm (ΔE∼36(ΔE∼36 and 34 meV) are presented, assuming either a- or c-plane crystal growth orientation. In the calculation of the quasibound state energies and wave functions, we account for the intrinsic electric field induced by piezoelectric and (in case of c-plane growth) the spontaneous polarization. The quantum-cascade structures were simulated, and their output characteristics extracted, using a fully self-consistent rate equation model with all relevant intra- and interperiod scatterings included. Both electron–LO-phonon and electron–electron scattering mechanisms are taken into account. Maximal population inversions between active laser states of up to 19% for the a-plane, and up to 40% for the c-plane design, are predicted and, based on estimated modal gain and waveguide/mirror losses in suitably designed structures, these indicate the feasibility of laser action in GaN/AlGaN cascades.