We make a detailed study on the angular differential cross sections of positron–hydrogen collisions by using the momentum-space coupled-channels optical (CCO) method for incident energies below the H ionization threshold. The target continuum and the positronium (Ps) formation channels are included in the coupled-channels calculations via a complex equivalent-local optical potential. The critical points, which show minima in the differential cross sections, as a function of the scattering angle and the incident energy are investigated. The resonances in the angular differential cross sections are reported for the first time in this energy range. The effects of the target continuum and the Ps formation channels on the different cross sections are discussed.