The charge distribution and potential profile of p-n-junctions in thin semiconductor nanowires (NWs) were analyzed. The characteristics of screening in one-dimensional systems result in a specific profile with large electric field at the boundary between the n- and p- regions, and long tails with a logarithmic drop in the potential and charge density. As a result of these tails, the junction properties depend sensitively on the geometry of external contacts and its capacity has an anomalously large value and frequency dispersion. In the presence of an external voltage, electrons and holes in the NWs can not be described by constant quasi-Fermi levels, due to small values of the average electric field, mobility, and lifetime of carriers. Thus, instead of the classical Sah-Noice-Shockley theory, the junction current-voltage characteristic was described by an alternative theory suitable for fast generation-recombination and slow diffusion-drift processes. For the non-uniform electric field in the junction, this theory predicts the forward branch of the characteristic to have a non-ideality factor η several times larger than the values 1 < η < 2 from classical theory. Such values of η have been experimentally observed by a number of researchers, as well as in the present work.