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We present the results of two-pion production in tagged quasi-free np collisions at a deutron incident beam energy of 1.25 GeV/c measured with the High-Acceptance Di-Electron Spectrometer (HADES) installed at GSI. The specific acceptance of HADES allowed for the first time to obtain high-precision data on π+π− and π−π0 production in np collisions in a region corresponding to large transverse momenta of the secondary particles. The obtained differential cross section data provide strong constraints on the production mechanisms and on the various baryon resonance contributions (∆∆, N(1440), N(1520), ∆(1600)). The invariant mass and angular distributions from the np → npπ+π −and np → ppπ−π0 reactions are compared with different theoretical model predictions.