Luminescence spectra of Light Emitting Diodes (LEDs) with Multiple Quantum Wells (MQWs) were studied at currents J = 0.15 μA - 150 mA. A high quantum efficiency at low J is caused by a low probability of the tunnel current J (which is maximum at Jm ≈ 0.5-1.0 mA). J(V) curves were measured in the range J= 10−12-10−1 A; at J > 10−3A they may be approximated by a sum of four parts: V= φk+ mkT·[ln(J/J0)+(J/J1)0.5] + J·Rs. The part V ~ (J/J1)0.5is the evidence of a double-injection into i-layers near MQWs. Their presence is confirmed by capacitance measurements. An overflow of carriers through the MQW causes a lower quantum efficiency at high J. A model of a 2D-density of states with exponential tails fits the spectra. The value of T in the active layer was estimated. A new band was detected at high J; it can be caused by non-uniformity of In content in MQWs.