We are investigating low-energy proton-antiproton-scattering cross sections in the framework of a potential model. The nucleon-antinucleon interaction is assumed to have two parts. The short-range annihilation part is derived from a non-relativistic quark model where nucleon-antinucleon transitions involving two- and three-meson final states are taken into account. The underlying quark dynamics is ruled by annihilation diagrams, where quark-antiquark pairs are created or destroyed with vacuum quantum numbers ( 3 P 0 in LS -coupling). The long- and medium-ranged elastic interaction is taken from a G -parity-transformed one-boson-exchange model for the nucleon-nucleon interaction. We present models, employing differing one-boson-exchange parts, as defined by the Bonn and the Paris potentials. We compare the results for the total, elastic, annihilation, charge-exchange and differential cross sections with the experimental data. We encounter an old shortcoming of microscopic models — albeit in a somewhat improved form: their inability to fully understand the total flux into the annihilation channels. We show that the annihilation cross section strongly depends on the elastic interaction.