Electroluminescence spectra of superbright blue and green LEDs based on epitaxial InxGa1−xN/AlyGa1−yN/GaN heterostructures with thin quantum well active layers  were studied at currents J = 0.01-20 mA. Spectral maxima of blue and green LEDs are ωmax = 2.58-2.75 eV and ωmax = 2.38-2.45 eV, dependent on the active layer In content. The low energy tails of the spectra are exponential with the parameter E0 = 42-50 meV almost independent of the temperature. The high energy tails of the spectra are exponential with a temperature dependent parameter E1= 20-40 meV. Both parameters (E0, E1) are current independent at J > 0.5 mA. The spectral band can be described by taking into account quantum size effects, impurities and electron-phonon interactions in active layers. A structure in the spectra was detected which can be described by the influence of light interference in the GaN layer on the sapphire substrate. Light intensity was a linear function of the drive current over the interval J = 1-20 mA, and was slightly temperature dependent. In the blue LEDs, the efficiency fall off at low currents (J < 0.7 mA) had a I ~ J4-5 dependence at room temperature. The green LEDs showed no such dependence. The influence of tunnel effects on the efficiency at low currents is discussed. Tunnel radiation spectra with maxima moving with the voltage were detected at low currents in III-N structures.