[en] We study the hard exclusive production of two pions in the virtual photon fragmentation region with various invariant masses including the resonance region. The amplitude is expressed in terms of two-pion light cone distribution amplitudes (2πDA's). We derive dispersion relations for these amplitudes, which enable us to fix them completely in terms of ππ scattering phases and a few low-energy subtraction constants determined by the effective chiral Lagrangian. Quantitative estimates of the resonance as well as ππ background DA's at low normalization point are made. We also prove a certain new soft pion theorem relating two-pion DA's to the one-pion DA. Crossing relations between 2πDA's and parton distributions in the pion are discussed. We demonstrate that by studying the shape of the ππ mass spectra (not the absolute cross section!) in diffractive electroproduction one can extract the deviation of the meson (π, π, etc.) wave functions from their asymptotic form 6z (1 - z) and hence get important information about the structure of mesons. Also we discuss how the moments of the quark distributions in the pion can be measured in the hard diffraction. We suggest (as an alternative to Soeding's) a parametrization of ππ spectra which is suitable for large photon virtuality