The production of photons at very small angles with respect to the proton beam direction is studied in deep-inelastic positron–proton scattering at HERA. The data are taken with the H1 detector in the years 2006 and 2007 and correspond to an integrated luminosity of 126 pb−1. The analysis covers the range of negative four momentum transfer squared at the positron vertex 6<Q 2<100 GeV2 and inelasticity 0.05<y<0.6. Cross sections are measured for the most energetic photon with pseudorapidity η>7.9
as a function of its transverse momentum pTlead and longitudinal momentum fraction of the incoming proton xLlead. In addition, the cross sections are studied as a function of the sum of the longitudinal momentum fraction xLsum of all photons in the pseudorapidity range η>7.9. The cross sections are normalised to the inclusive deep-inelastic scattering cross section and compared to the predictions of models of deep-inelastic scattering and models of the hadronic interactions of high energy cosmic rays.