We have developed a model for the N N → N N ππ reaction and evaluated cross sections for the different charged channels. The low energy part of those channels where the pions can be in an isospin zero state is dominated by N * excitation, driven by an isoscalar source recently found experimentally, followed by the decay N * → N (ππ) T =0 S−wave . At higher energies, and in channels where the pions are not in T=0, ∆ excitation mechanisms become relevant. A rough agreement with the experimental data is obtained in most channels. Repercussions of the present findings for the ABC effect and the pp → ppπ 0 reaction close to threshold are also suggested.