Organic electroluminescent device having an emission maximum of ≤ 570 nm comprising, in this sequence, an anode, an electron-blocking layer, a phosphorescent emission layer which comprises at least one phosphorescent compound and at least one matrix material, where the total concentration of all phosphorescent compounds is < 10% by vol., a hole-blocking layer and a cathode, where the electroluminescent device comprises no aluminium metal complex between the emitting layer and the cathode, characterised in that the following applies to the layers: a) HOMO EBL − HOMO EML ≤ 0.4 eV; b) LUMO EML − LUMO HBL ≤ 0.4 eV; c) HOMO of all matrix mateirals of the EML ≥ − 6.0 eV; and d) LUMO EML ≤ − 2.5 eV; where HOMO represents the HOMO of the material of the electron-blocking layer, HOMO represents the HOMO of the matrix material of the emission layer, LUMO represents the LUMO of the matrix material of the emission layer and LUMO represents the LUMO of the material of the hole-blocking layer; on use of a plurality of matrix materials, HOMO is the highest HOMO of the matrix components and LUMO is the lowest LUMO of the matrix components; the HOMO and LUMO positions are determined as follows via quantum-chemical calculations using the "Gaussian03W" software package (Gaussian Inc.): for the calculation of organic substances without metals, firstly a geometry optimisation is carried out using the "Ground State/Semi-empirical/Default Spin/AM1/Charge 0/Spin Singlet" method, followed by an energy calculation on the basis of the optimised geometry using the "TD-SFC/DFT/Default Spin/B3PW91" method with the "6-31G(d)" base set (Charge 0, Spin Singlet); for organometallic compounds, the geometry is optimised via the "Ground State/Hartree-Fock/Default Spin/LanL2MB/Charge 0/Spin Singlet" method, followed by an energy calculation analogously to the organic substances, as described above, with the difference that the "LanL2DZ" base set is used for the metal atom and the "6-31G(d)" base set is used for the ligands; the HOMO and LUMO values in electron volts are determined in accordance with the following formula from the HOMO HEh or LUMO LEh in hartree units obtained from the energy calculation: HOMO eV = HEh * 27.212 − 0.9899 / 1.1206 LUMO eV = LEh * 27.212 − 2.0041 / 1.385. a) HOMO EBL − HOMO EML ≤ 0.4 eV; b) LUMO EML − LUMO HBL ≤ 0.4 eV; c) HOMO of all matrix mateirals of the EML ≥ − 6.0 eV; and d) LUMO EML ≤ − 2.5 eV; where HOMO represents the HOMO of the material of the electron-blocking layer, HOMO represents the HOMO of the matrix material of the emission layer, LUMO represents the LUMO of the matrix material of the emission layer and LUMO represents the LUMO of the material of the hole-blocking layer; on use of a plurality of matrix materials, HOMO is the highest HOMO of the matrix components and LUMO is the lowest LUMO of the matrix components; the HOMO and LUMO positions are determined as follows via quantum-chemical calculations using the "Gaussian03W" software package (Gaussian Inc.): for the calculation of organic substances without metals, firstly a geometry optimisation is carried out using the "Ground State/Semi-empirical/Default Spin/AM1/Charge 0/Spin Singlet" method, followed by an energy calculation on the basis of the optimised geometry using the "TD-SFC/DFT/Default Spin/B3PW91" method with the "6-31G(d)" base set (Charge 0, Spin Singlet); for organometallic compounds, the geometry is optimised via the "Ground State/Hartree-Fock/Default Spin/LanL2MB/Charge 0/Spin Singlet" method, followed by an energy calculation analogously to the organic substances, as described above, with the difference that the "LanL2DZ" base set is used for the metal atom and the "6-31G(d)" base set is used for the ligands; the HOMO and LUMO values in electron volts are determined in accordance with the following formula from the HOMO HEh or LUMO LEh in hartree units obtained from the energy calculation: HOMO eV = HEh * 27.212 − 0.9899 / 1.1206 LUMO eV = LEh * 27.212 − 2.0041 / 1.385. where HOMO represents the HOMO of the material of the electron-blocking layer, HOMO represents the HOMO of the matrix material of the emission layer, LUMO represents the LUMO of the matrix material of the emission layer and LUMO represents the LUMO of the material of the hole-blocking layer; on use of a plurality of matrix materials, HOMO is the highest HOMO of the matrix components and LUMO is the lowest LUMO of the matrix components; the HOMO and LUMO positions are determined as follows via quantum-chemical calculations using the "Gaussian03W" software package (Gaussian Inc.): for the calculation of organic substances without metals, firstly a geometry optimisation is carried out using the "Ground State/Semi-empirical/Default Spin/AM1/Charge 0/Spin Singlet" method, followed by an energy calculation on the basis of the optimised geometry using the "TD-SFC/DFT/Default Spin/B3PW91" method with the "6-31G(d)" base set (Charge 0, Spin Singlet); for organometallic compounds, the geometry is optimised via the "Ground State/Hartree-Fock/Default Spin/LanL2MB/Charge 0/Spin Singlet" method, followed by an energy calculation analogously to the organic substances, as described above, with the difference that the "LanL2DZ" base set is used for the metal atom and the "6-31G(d)" base set is used for the ligands; the HOMO and LUMO values in electron volts are determined in accordance with the following formula from the HOMO HEh or LUMO LEh in hartree units obtained from the energy calculation: HOMO eV = HEh * 27.212 − 0.9899 / 1.1206 LUMO eV = LEh * 27.212 − 2.0041 / 1.385.