The np → npπ + π − reaction has been studied at the incident neutron energies of 1.0 GeV and 1.5 GeV in 4π-geometry using the neutron beam produced by the breakup of the relativistic deuterons at the JINR Synchrophasotron. The np → npπ + π − data obtained at 1.5 GeV demonstrate the dominance of the ΔΔ excitation process with a significant contribution of the higher-lying baryonic resonances, while the data at 1.0 GeV show a non-resonant behavior. The angular and mass distributions are compared with the predictions of different models suggested for the double pion production in the NN collisions. The calculations performed within the model based on the reggeized π-exchange taking one baryon exchange into account are in good agreement with the experimental data obtained at both energies.